/*************************************************************************/ /* Author : Gonzalo Tornaria * Date : December 2003 */ /* * All isogeny classes of elliptic curves of prime conductor less than 20000: * * [name, level, degree, equation] * * name : name of the class, (following Cremona) * level : conductor of the curve * degree : modular degree of optimal curve * equation : equation of optimal curve * * data from 'Elliptic Curve Data' by J. E. Cremona, * * * for an interactive version see: * * */ /*************************************************************************/ ell_11A = ["11A", 11, 1, [0,-1,1,-10,-20]]; ell_17A = ["17A", 17, 1, [1,-1,1,-1,-14]]; ell_19A = ["19A", 19, 1, [0,1,1,-9,-15]]; ell_37A = ["37A", 37, 2, [0,0,1,-1,0]]; ell_37B = ["37B", 37, 2, [0,1,1,-23,-50]]; ell_43A = ["43A", 43, 2, [0,1,1,0,0]]; ell_53A = ["53A", 53, 2, [1,-1,1,0,0]]; ell_61A = ["61A", 61, 2, [1,0,0,-2,1]]; ell_67A = ["67A", 67, 5, [0,1,1,-12,-21]]; ell_73A = ["73A", 73, 3, [1,-1,0,4,-3]]; ell_79A = ["79A", 79, 2, [1,1,1,-2,0]]; ell_83A = ["83A", 83, 2, [1,1,1,1,0]]; ell_89A = ["89A", 89, 2, [1,1,1,-1,0]]; ell_89B = ["89B", 89, 5, [1,1,0,4,5]]; ell_101A = ["101A", 101, 2, [0,1,1,-1,-1]]; ell_109A = ["109A", 109, 4, [1,-1,0,-8,-7]]; ell_113A = ["113A", 113, 6, [1,1,1,3,-4]]; ell_131A = ["131A", 131, 2, [0,-1,1,1,0]]; ell_139A = ["139A", 139, 6, [1,1,0,-3,-4]]; ell_163A = ["163A", 163, 6, [0,0,1,-2,1]]; ell_179A = ["179A", 179, 9, [0,0,1,-1,-1]]; ell_197A = ["197A", 197, 10, [0,0,1,-5,4]]; ell_229A = ["229A", 229, 8, [1,0,0,-2,-1]]; ell_233A = ["233A", 233, 27, [1,0,1,0,11]]; ell_269A = ["269A", 269, 6, [0,0,1,-2,-1]]; ell_277A = ["277A", 277, 10, [1,0,1,0,-1]]; ell_307A = ["307A", 307, 13, [0,0,1,-8,-9]]; ell_307B = ["307B", 307, 10, [1,1,0,0,-1]]; ell_307C = ["307C", 307, 11, [0,0,1,1,-1]]; ell_307D = ["307D", 307, 15, [0,-1,1,2,-1]]; ell_331A = ["331A", 331, 12, [1,0,0,-5,4]]; ell_347A = ["347A", 347, 14, [0,1,1,2,0]]; ell_353A = ["353A", 353, 24, [1,1,1,-2,16]]; ell_359A = ["359A", 359, 16, [1,0,1,-23,39]]; ell_359B = ["359B", 359, 8, [1,-1,1,-7,8]]; ell_373A = ["373A", 373, 22, [0,1,1,-2,-2]]; ell_389A = ["389A", 389, 40, [0,1,1,-2,0]]; ell_431A = ["431A", 431, 10, [1,0,0,0,-1]]; ell_431B = ["431B", 431, 40, [1,-1,1,-9,-8]]; ell_433A = ["433A", 433, 28, [1,0,0,0,1]]; ell_443A = ["443A", 443, 12, [0,1,1,1,1]]; ell_443B = ["443B", 443, 14, [1,0,0,-3,-2]]; ell_443C = ["443C", 443, 62, [1,0,1,-84,-301]]; ell_467A = ["467A", 467, 34, [0,0,1,-4,3]]; ell_503A = ["503A", 503, 22, [1,0,1,-32,-71]]; ell_503B = ["503B", 503, 38, [1,-1,0,2,-1]]; ell_503C = ["503C", 503, 100, [1,0,0,-210,-1189]]; ell_557A = ["557A", 557, 14, [1,1,0,0,1]]; ell_557B = ["557B", 557, 182, [0,-1,1,-268,1781]]; ell_563A = ["563A", 563, 52, [1,1,1,-15,16]]; ell_571A = ["571A", 571, 120, [0,-1,1,-929,-10595]]; ell_571B = ["571B", 571, 48, [0,1,1,-4,2]]; ell_593A = ["593A", 593, 22, [1,0,1,-2,1]]; ell_593B = ["593B", 593, 58, [1,0,0,-7,-30]]; ell_643A = ["643A", 643, 32, [1,0,0,-4,3]]; ell_659A = ["659A", 659, 50, [1,1,0,-79,-306]]; ell_659B = ["659B", 659, 141, [0,1,1,-372,2641]]; ell_677A = ["677A", 677, 22, [1,1,1,2,0]]; ell_701A = ["701A", 701, 42, [0,-1,1,-2,1]]; ell_709A = ["709A", 709, 44, [0,-1,1,-2,0]]; ell_733A = ["733A", 733, 48, [1,1,0,-75,-284]]; ell_739A = ["739A", 739, 33, [0,0,1,1,1]]; ell_797A = ["797A", 797, 24, [1,0,0,2,1]]; ell_811A = ["811A", 811, 24, [0,0,1,-2,-2]]; ell_827A = ["827A", 827, 44, [0,0,1,-10,12]]; ell_829A = ["829A", 829, 66, [0,0,1,-4,-3]]; ell_997A = ["997A", 997, 80, [0,-1,1,-18,36]]; ell_997B = ["997B", 997, 48, [0,-1,1,-5,-3]]; ell_997C = ["997C", 997, 96, [0,-1,1,-24,54]]; ell_1019A = ["1019A", 1019, 192, [0,1,1,-1961,32779]]; ell_1019B = ["1019B", 1019, 72, [0,1,1,-6,4]]; ell_1051A = ["1051A", 1051, 40, [0,1,1,-5,3]]; ell_1091A = ["1091A", 1091, 38, [1,0,0,-4,-3]]; ell_1153A = ["1153A", 1153, 96, [1,-1,1,-19,68]]; ell_1171A = ["1171A", 1171, 88, [1,-1,1,-3,0]]; ell_1171B = ["1171B", 1171, 81, [0,-1,1,-4,5]]; ell_1187A = ["1187A", 1187, 117, [0,0,1,2,1]]; ell_1187B = ["1187B", 1187, 80, [1,-1,1,0,-2]]; ell_1187C = ["1187C", 1187, 91, [0,1,1,-22,33]]; ell_1259A = ["1259A", 1259, 30, [0,1,1,3,1]]; ell_1259B = ["1259B", 1259, 68, [1,-1,1,-3,-2]]; ell_1259C = ["1259C", 1259, 159, [0,0,1,-1,-2]]; ell_1289A = ["1289A", 1289, 219, [1,0,1,-22,-75]]; ell_1297A = ["1297A", 1297, 40, [1,1,0,1,2]]; ell_1321A = ["1321A", 1321, 88, [1,1,0,3,2]]; ell_1373A = ["1373A", 1373, 52, [1,0,0,-18,-31]]; ell_1433A = ["1433A", 1433, 165, [1,0,1,-25,81]]; ell_1439A = ["1439A", 1439, 38, [1,1,0,2,-1]]; ell_1483A = ["1483A", 1483, 120, [0,1,1,2,2]]; ell_1531A = ["1531A", 1531, 96, [0,0,1,-14,20]]; ell_1549A = ["1549A", 1549, 54, [1,-1,1,-1,-2]]; ell_1607A = ["1607A", 1607, 50, [1,0,0,-7,-8]]; ell_1613A = ["1613A", 1613, 80, [0,1,1,-3,0]]; ell_1613B = ["1613B", 1613, 304, [0,-1,1,-92,-311]]; ell_1621A = ["1621A", 1621, 68, [1,-1,1,-4,4]]; ell_1627A = ["1627A", 1627, 72, [1,1,1,-3,-2]]; ell_1747A = ["1747A", 1747, 90, [0,0,1,-5,-5]]; ell_1811A = ["1811A", 1811, 62, [0,-1,1,3,0]]; ell_1867A = ["1867A", 1867, 177, [0,-1,1,-2,-2]]; ell_1873A = ["1873A", 1873, 64, [1,-1,1,-1,2]]; ell_1901A = ["1901A", 1901, 116, [1,1,0,-29,-74]]; ell_1907A = ["1907A", 1907, 112, [1,-1,1,-46,130]]; ell_1907B = ["1907B", 1907, 165, [0,-1,1,-2,3]]; ell_1913A = ["1913A", 1913, 300, [1,1,0,-202,1025]]; ell_1913B = ["1913B", 1913, 309, [1,1,0,-34,-135]]; ell_1933A = ["1933A", 1933, 84, [1,0,0,1,-2]]; ell_1949A = ["1949A", 1949, 114, [0,1,1,-7,-10]]; ell_1973A = ["1973A", 1973, 126, [0,1,1,-8,-12]]; ell_1979A = ["1979A", 1979, 55, [0,0,1,-4,-4]]; ell_1987A = ["1987A", 1987, 62, [0,-1,1,-3,4]]; ell_2017A = ["2017A", 2017, 102, [1,1,0,-10,9]]; ell_2027A = ["2027A", 2027, 116, [0,-1,1,-8,12]]; ell_2089A = ["2089A", 2089, 84, [1,1,1,-5,-6]]; ell_2089B = ["2089B", 2089, 219, [1,-1,0,-38,145]]; ell_2089C = ["2089C", 2089, 228, [1,0,1,-20,-35]]; ell_2089D = ["2089D", 2089, 480, [1,-1,0,-214,-1153]]; ell_2089E = ["2089E", 2089, 352, [1,-1,1,-39,102]]; ell_2141A = ["2141A", 2141, 206, [1,-1,0,-1,-2]]; ell_2143A = ["2143A", 2143, 216, [1,-1,0,-16,29]]; ell_2161A = ["2161A", 2161, 54, [1,-1,0,1,2]]; ell_2213A = ["2213A", 2213, 152, [1,-1,0,-26,-45]]; ell_2221A = ["2221A", 2221, 54, [0,-1,1,-11,18]]; ell_2237A = ["2237A", 2237, 116, [1,1,0,1,-2]]; ell_2251A = ["2251A", 2251, 148, [0,0,1,1,2]]; ell_2269A = ["2269A", 2269, 98, [0,0,1,-7,-7]]; ell_2273A = ["2273A", 2273, 392, [1,0,0,-42,-155]]; ell_2341A = ["2341A", 2341, 138, [0,1,1,-6,-8]]; ell_2351A = ["2351A", 2351, 138, [1,0,1,-5,-5]]; ell_2357A = ["2357A", 2357, 70, [0,-1,1,-3,1]]; ell_2393A = ["2393A", 2393, 80, [1,-1,0,-7,-6]]; ell_2539A = ["2539A", 2539, 160, [0,0,1,-11,14]]; ell_2557A = ["2557A", 2557, 156, [1,0,0,-5,-4]]; ell_2609A = ["2609A", 2609, 110, [1,1,0,-1,2]]; ell_2677A = ["2677A", 2677, 96, [1,1,1,-4,0]]; ell_2699A = ["2699A", 2699, 70, [0,0,1,2,2]]; ell_2699B = ["2699B", 2699, 171, [0,-1,1,1,-3]]; ell_2699C = ["2699C", 2699, 413, [0,0,1,-88,-318]]; ell_2749A = ["2749A", 2749, 122, [1,0,1,-2,-3]]; ell_2797A = ["2797A", 2797, 176, [0,1,1,-9,-14]]; ell_2837A = ["2837A", 2837, 184, [0,1,1,-4,-4]]; ell_2843A = ["2843A", 2843, 448, [1,-1,1,3,0]]; ell_2917A = ["2917A", 2917, 444, [1,-1,0,-4,-1]]; ell_2939A = ["2939A", 2939, 205, [0,1,1,-4,-6]]; ell_2953A = ["2953A", 2953, 116, [1,0,0,-9,10]]; ell_3023A = ["3023A", 3023, 98, [1,-1,1,-4,0]]; ell_3089A = ["3089A", 3089, 710, [1,1,1,-59,-254]]; ell_3109A = ["3109A", 3109, 138, [0,-1,1,-7,-5]]; ell_3163A = ["3163A", 3163, 144, [1,0,1,3,-1]]; ell_3181A = ["3181A", 3181, 218, [0,1,1,-49,-150]]; ell_3203A = ["3203A", 3203, 401, [0,0,1,-1,-3]]; ell_3229A = ["3229A", 3229, 104, [1,1,1,-9,-14]]; ell_3251A = ["3251A", 3251, 322, [0,-1,1,-37,100]]; ell_3257A = ["3257A", 3257, 280, [1,0,1,-9,9]]; ell_3259A = ["3259A", 3259, 290, [0,-1,1,4,-2]]; ell_3259B = ["3259B", 3259, 510, [0,-1,1,-54,172]]; ell_3259C = ["3259C", 3259, 149, [0,-1,1,3,1]]; ell_3313A = ["3313A", 3313, 162, [1,0,1,-6,5]]; ell_3313B = ["3313B", 3313, 650, [1,-1,1,-64,268]]; ell_3331A = ["3331A", 3331, 263, [0,0,1,1,-3]]; ell_3347A = ["3347A", 3347, 130, [0,1,1,2,3]]; ell_3371A = ["3371A", 3371, 247, [0,-1,1,-25,-41]]; ell_3371B = ["3371B", 3371, 186, [1,0,1,0,-3]]; ell_3391A = ["3391A", 3391, 160, [1,0,0,-4,1]]; ell_3467A = ["3467A", 3467, 117, [0,1,1,-3,-5]]; ell_3469A = ["3469A", 3469, 270, [1,0,0,-26,49]]; ell_3547A = ["3547A", 3547, 164, [0,1,1,3,3]]; ell_3547B = ["3547B", 3547, 102, [1,-1,0,4,-1]]; ell_3547C = ["3547C", 3547, 409, [0,0,1,-35,-80]]; ell_3623A = ["3623A", 3623, 162, [1,1,0,-5,-8]]; ell_3779A = ["3779A", 3779, 292, [0,0,1,2,-3]]; ell_3797A = ["3797A", 3797, 568, [0,0,1,-71,230]]; ell_3803A = ["3803A", 3803, 492, [1,0,1,-581,5335]]; ell_3851A = ["3851A", 3851, 578, [0,-1,1,-92,372]]; ell_3853A = ["3853A", 3853, 162, [0,0,1,-4,-1]]; ell_3877A = ["3877A", 3877, 186, [1,0,0,3,-2]]; ell_3907A = ["3907A", 3907, 171, [0,0,1,-5,5]]; ell_3931A = ["3931A", 3931, 184, [0,1,1,1,-3]]; ell_3947A = ["3947A", 3947, 90, [0,-1,1,-3,-3]]; ell_3967A = ["3967A", 3967, 156, [1,0,0,2,3]]; ell_4013A = ["4013A", 4013, 430, [0,1,1,-6,3]]; ell_4021A = ["4021A", 4021, 422, [0,1,1,-4,0]]; ell_4051A = ["4051A", 4051, 90, [0,0,1,-2,3]]; ell_4139A = ["4139A", 4139, 268, [0,-1,1,4,0]]; ell_4159A = ["4159A", 4159, 200, [1,1,0,-11,10]]; ell_4159B = ["4159B", 4159, 3504, [1,-1,0,-7303,242050]]; ell_4229A = ["4229A", 4229, 2184, [1,-1,1,-2091,-36272]]; ell_4283A = ["4283A", 4283, 274, [1,-1,0,-5,-2]]; ell_4289A = ["4289A", 4289, 872, [1,1,1,-84,326]]; ell_4337A = ["4337A", 4337, 704, [1,-1,1,-3,4]]; ell_4339A = ["4339A", 4339, 223, [0,0,1,4,-1]]; ell_4357A = ["4357A", 4357, 364, [0,0,1,-10,-12]]; ell_4451A = ["4451A", 4451, 327, [0,-1,1,-2,-3]]; ell_4457A = ["4457A", 4457, 156, [1,0,1,0,3]]; ell_4481A = ["4481A", 4481, 784, [1,0,1,-197,-1077]]; ell_4481B = ["4481B", 4481, 196, [1,1,1,-6,2]]; ell_4481C = ["4481C", 4481, 180, [1,-1,1,-13,20]]; ell_4493A = ["4493A", 4493, 260, [1,0,0,-32,67]]; ell_4507A = ["4507A", 4507, 374, [0,-1,1,-2,4]]; ell_4547A = ["4547A", 4547, 292, [0,-1,1,-43,124]]; ell_4603A = ["4603A", 4603, 340, [0,-1,1,2,-4]]; ell_4733A = ["4733A", 4733, 318, [0,0,1,-5,-3]]; ell_4799A = ["4799A", 4799, 304, [1,0,0,4,-1]]; ell_4799B = ["4799B", 4799, 312, [1,1,1,-19,24]]; ell_4799C = ["4799C", 4799, 336, [1,0,0,-31,64]]; ell_5021A = ["5021A", 5021, 518, [0,1,1,-4,-1]]; ell_5077A = ["5077A", 5077, 1984, [0,0,1,-7,6]]; ell_5171A = ["5171A", 5171, 292, [0,1,1,-17,22]]; ell_5197A = ["5197A", 5197, 490, [0,-1,1,-4,1]]; ell_5237A = ["5237A", 5237, 234, [0,0,1,-20,34]]; ell_5303A = ["5303A", 5303, 434, [1,1,0,-4,-3]]; ell_5309A = ["5309A", 5309, 302, [0,0,1,-17,-27]]; ell_5393A = ["5393A", 5393, 1142, [1,0,0,-107,490]]; ell_5417A = ["5417A", 5417, 430, [1,-1,0,-7,10]]; ell_5417B = ["5417B", 5417, 2496, [1,0,0,-13012,570217]]; ell_5417C = ["5417C", 5417, 224, [1,1,1,3,4]]; ell_5419A = ["5419A", 5419, 245, [0,0,1,4,-2]]; ell_5443A = ["5443A", 5443, 546, [0,-1,1,-28,-49]]; ell_5443B = ["5443B", 5443, 186, [1,1,0,4,-1]]; ell_5503A = ["5503A", 5503, 1264, [1,0,0,-2893,-60134]]; ell_5563A = ["5563A", 5563, 308, [0,0,1,-2,-4]]; ell_5651A = ["5651A", 5651, 701, [0,0,1,-4,-5]]; ell_5653A = ["5653A", 5653, 336, [1,-1,1,-10,-10]]; ell_5689A = ["5689A", 5689, 1601, [1,-1,0,-113,-510]]; ell_5717A = ["5717A", 5717, 392, [1,1,0,-4,-7]]; ell_5741A = ["5741A", 5741, 288, [1,-1,0,-5,4]]; ell_5813A = ["5813A", 5813, 296, [0,0,1,-5,2]]; ell_5867A = ["5867A", 5867, 420, [1,-1,0,-1,4]]; ell_5987A = ["5987A", 5987, 228, [1,1,0,-5,4]]; ell_5987B = ["5987B", 5987, 205, [0,1,1,3,4]]; ell_5987C = ["5987C", 5987, 897, [0,-1,1,-6,9]]; ell_6011A = ["6011A", 6011, 198, [1,1,0,1,4]]; ell_6011B = ["6011B", 6011, 917, [0,0,1,-172,868]]; ell_6011C = ["6011C", 6011, 308, [0,0,1,-1,-4]]; ell_6043A = ["6043A", 6043, 216, [1,0,0,-3,4]]; ell_6067A = ["6067A", 6067, 515, [0,1,1,-2,3]]; ell_6131A = ["6131A", 6131, 492, [0,1,1,-2,-5]]; ell_6199A = ["6199A", 6199, 308, [1,1,1,1,4]]; ell_6199B = ["6199B", 6199, 660, [1,0,0,-146,667]]; ell_6211A = ["6211A", 6211, 194, [1,-1,0,1,-4]]; ell_6323A = ["6323A", 6323, 746, [1,0,1,-58,-173]]; ell_6373A = ["6373A", 6373, 392, [0,-1,1,-17,33]]; ell_6427A = ["6427A", 6427, 506, [1,1,0,-7,-10]]; ell_6451A = ["6451A", 6451, 2340, [0,1,1,-242,-1533]]; ell_6571A = ["6571A", 6571, 192, [1,-1,1,-1,-4]]; ell_6689A = ["6689A", 6689, 346, [1,0,1,3,-3]]; ell_6691A = ["6691A", 6691, 330, [0,1,1,5,2]]; ell_6691B = ["6691B", 6691, 312, [1,0,0,1,4]]; ell_6823A = ["6823A", 6823, 774, [1,-1,1,-385,3000]]; ell_6899A = ["6899A", 6899, 451, [0,1,1,1,4]]; ell_6911A = ["6911A", 6911, 776, [1,1,1,-250,-1626]]; ell_6967A = ["6967A", 6967, 292, [1,-1,0,-17,32]]; ell_7019A = ["7019A", 7019, 288, [0,1,1,4,4]]; ell_7019B = ["7019B", 7019, 360, [1,0,0,-5,-2]]; ell_7057A = ["7057A", 7057, 2736, [1,1,0,-9195,-343232]]; ell_7057B = ["7057B", 7057, 528, [1,-1,0,-7,8]]; ell_7057C = ["7057C", 7057, 976, [1,0,0,-438,-3565]]; ell_7057D = ["7057D", 7057, 1136, [1,-1,1,-75,-230]]; ell_7109A = ["7109A", 7109, 450, [0,0,1,-14,-20]]; ell_7109B = ["7109B", 7109, 394, [1,1,0,-13,14]]; ell_7187A = ["7187A", 7187, 984, [0,1,1,-192,-1091]]; ell_7213A = ["7213A", 7213, 518, [0,-1,1,-117,528]]; ell_7219A = ["7219A", 7219, 220, [1,-1,1,-1,4]]; ell_7283A = ["7283A", 7283, 676, [0,1,1,5,0]]; ell_7451A = ["7451A", 7451, 732, [0,0,1,-7,8]]; ell_7541A = ["7541A", 7541, 620, [0,0,1,-23,42]]; ell_7669A = ["7669A", 7669, 1356, [0,0,1,-7,-6]]; ell_7691A = ["7691A", 7691, 345, [0,1,1,5,3]]; ell_7699A = ["7699A", 7699, 580, [1,1,0,-16,-33]]; ell_7723A = ["7723A", 7723, 398, [1,-1,0,1,4]]; ell_7723B = ["7723B", 7723, 891, [0,0,1,-65,-202]]; ell_7757A = ["7757A", 7757, 474, [0,0,1,-5,-1]]; ell_7841A = ["7841A", 7841, 636, [1,1,1,-160,-846]]; ell_7867A = ["7867A", 7867, 560, [0,0,1,1,4]]; ell_8069A = ["8069A", 8069, 432, [1,1,1,-5,-2]]; ell_8101A = ["8101A", 8101, 0, [0,0,1,-16,24]]; ell_8167A = ["8167A", 8167, 0, [1,0,1,-14,-21]]; ell_8219A = ["8219A", 8219, 0, [0,-1,1,-21,45]]; ell_8237A = ["8237A", 8237, 0, [1,1,0,2,5]]; ell_8243A = ["8243A", 8243, 0, [0,0,1,5,-1]]; ell_8363A = ["8363A", 8363, 0, [0,-1,1,-9,-9]]; ell_8363B = ["8363B", 8363, 0, [1,0,1,-86,297]]; ell_8419A = ["8419A", 8419, 0, [0,-1,1,4,-5]]; ell_8443A = ["8443A", 8443, 0, [0,1,1,2,-4]]; ell_8539A = ["8539A", 8539, 0, [0,-1,1,-7,11]]; ell_8543A = ["8543A", 8543, 0, [1,1,0,-8,5]]; ell_8597A = ["8597A", 8597, 0, [1,1,1,-8,4]]; ell_8623A = ["8623A", 8623, 0, [1,0,1,-11,-15]]; ell_8623B = ["8623B", 8623, 0, [1,1,0,-32,-85]]; ell_8699A = ["8699A", 8699, 0, [0,1,1,-31,57]]; ell_8713A = ["8713A", 8713, 0, [1,-1,0,-176,1037]]; ell_8731A = ["8731A", 8731, 0, [0,-1,1,1,-5]]; ell_8747A = ["8747A", 8747, 0, [0,-1,1,-111,489]]; ell_8747B = ["8747B", 8747, 0, [0,-1,1,3,3]]; ell_8747C = ["8747C", 8747, 0, [0,0,1,-205,-1130]]; ell_8747D = ["8747D", 8747, 0, [0,0,1,-1609,-24842]]; ell_8803A = ["8803A", 8803, 0, [0,-1,1,1,4]]; ell_8803B = ["8803B", 8803, 0, [0,0,1,-11,-15]]; ell_8861A = ["8861A", 8861, 0, [0,-1,1,-7,-4]]; ell_8929A = ["8929A", 8929, 0, [1,-1,1,-16,28]]; ell_8999A = ["8999A", 8999, 0, [1,-1,1,-97,-342]]; ell_9011A = ["9011A", 9011, 0, [1,0,1,-2,-5]]; ell_9109A = ["9109A", 9109, 0, [0,1,1,-20,28]]; ell_9127A = ["9127A", 9127, 0, [1,-1,1,-40,106]]; ell_9127B = ["9127B", 9127, 0, [1,-1,1,-4,6]]; ell_9151A = ["9151A", 9151, 0, [1,0,1,-20,31]]; ell_9161A = ["9161A", 9161, 0, [1,0,0,-17,26]]; ell_9203A = ["9203A", 9203, 0, [0,-1,1,-3,6]]; ell_9277A = ["9277A", 9277, 0, [0,-1,1,-13,-14]]; ell_9323A = ["9323A", 9323, 0, [0,0,1,5,-2]]; ell_9341A = ["9341A", 9341, 0, [0,0,1,-11,13]]; ell_9413A = ["9413A", 9413, 0, [1,1,0,-5,-4]]; ell_9467A = ["9467A", 9467, 0, [1,0,0,-19,30]]; ell_9473A = ["9473A", 9473, 0, [1,0,0,-192,1105]]; ell_9479A = ["9479A", 9479, 0, [1,0,0,-7,-6]]; ell_9491A = ["9491A", 9491, 0, [1,0,0,3,-4]]; ell_9539A = ["9539A", 9539, 0, [0,-1,1,-4,7]]; ell_9551A = ["9551A", 9551, 0, [1,1,0,-6,-7]]; ell_9587A = ["9587A", 9587, 0, [0,1,1,-12,13]]; ell_9661A = ["9661A", 9661, 0, [0,1,1,-31,-78]]; ell_9811A = ["9811A", 9811, 0, [0,0,1,-26,51]]; ell_9811B = ["9811B", 9811, 0, [1,1,1,5,4]]; ell_9811C = ["9811C", 9811, 0, [0,0,1,1,-5]]; ell_9829A = ["9829A", 9829, 0, [0,0,1,-187,984]]; ell_9829B = ["9829B", 9829, 0, [0,0,1,-52,144]]; ell_9829C = ["9829C", 9829, 0, [0,1,1,-22,-48]]; ell_9901A = ["9901A", 9901, 0, [0,0,1,-373,-2773]]; ell_9923A = ["9923A", 9923, 0, [0,1,1,-13,-24]]; ell_9941A = ["9941A", 9941, 0, [0,-1,1,-6,-2]]; ell_9967A = ["9967A", 9967, 0, [1,0,1,4,-3]]; ell_10061A = ["10061A", 10061, 0, [0,0,1,-8,7]]; ell_10079A = ["10079A", 10079, 0, [1,-1,1,-33,80]]; ell_10091A = ["10091A", 10091, 0, [1,0,0,-74,239]]; ell_10099A = ["10099A", 10099, 0, [1,0,1,-7,-5]]; ell_10099B = ["10099B", 10099, 0, [0,1,1,4,-3]]; ell_10163A = ["10163A", 10163, 0, [1,0,1,-381,-2889]]; ell_10259A = ["10259A", 10259, 0, [0,0,1,2,-5]]; ell_10331A = ["10331A", 10331, 0, [0,0,1,-19,32]]; ell_10333A = ["10333A", 10333, 0, [0,0,1,-139,-631]]; ell_10333B = ["10333B", 10333, 0, [0,-1,1,-28,67]]; ell_10333C = ["10333C", 10333, 0, [0,0,1,-40,97]]; ell_10333D = ["10333D", 10333, 0, [0,0,1,-94,-351]]; ell_10333E = ["10333E", 10333, 0, [1,0,0,-17,-28]]; ell_10357A = ["10357A", 10357, 0, [1,1,1,-2,4]]; ell_10427A = ["10427A", 10427, 0, [0,-1,1,2,4]]; ell_10499A = ["10499A", 10499, 0, [0,-1,1,-11,-12]]; ell_10567A = ["10567A", 10567, 0, [1,-1,0,4,-5]]; ell_10567B = ["10567B", 10567, 0, [1,-1,0,-5,8]]; ell_10597A = ["10597A", 10597, 0, [0,1,1,-19,-39]]; ell_10639A = ["10639A", 10639, 0, [1,1,1,-4,4]]; ell_10691A = ["10691A", 10691, 0, [1,-1,0,-4,7]]; ell_10733A = ["10733A", 10733, 0, [1,0,1,-6,-1]]; ell_10789A = ["10789A", 10789, 0, [0,1,1,-37,75]]; ell_10799A = ["10799A", 10799, 0, [1,0,1,5,1]]; ell_10859A = ["10859A", 10859, 0, [0,1,1,1,-5]]; ell_10859B = ["10859B", 10859, 0, [0,1,1,-356,-2708]]; ell_10949A = ["10949A", 10949, 0, [1,0,1,-13,15]]; ell_10957A = ["10957A", 10957, 0, [1,1,1,-12,-22]]; ell_10979A = ["10979A", 10979, 0, [0,0,1,-28,57]]; ell_10987A = ["10987A", 10987, 0, [0,-1,1,-7,-7]]; ell_11003A = ["11003A", 11003, 0, [1,1,1,-3,4]]; ell_11059A = ["11059A", 11059, 0, [0,-1,1,-14,-17]]; ell_11119A = ["11119A", 11119, 0, [1,1,0,-9,-14]]; ell_11171A = ["11171A", 11171, 0, [0,-1,1,-4,-5]]; ell_11177A = ["11177A", 11177, 0, [1,-1,1,-45,126]]; ell_11197A = ["11197A", 11197, 0, [1,-1,1,-6,0]]; ell_11251A = ["11251A", 11251, 0, [0,1,1,-25,-58]]; ell_11321A = ["11321A", 11321, 0, [1,1,0,6,1]]; ell_11321B = ["11321B", 11321, 0, [1,1,0,-13,-24]]; ell_11321C = ["11321C", 11321, 0, [1,0,0,-26,-53]]; ell_11353A = ["11353A", 11353, 0, [1,0,1,-7,-9]]; ell_11467A = ["11467A", 11467, 0, [1,-1,1,-6,2]]; ell_11483A = ["11483A", 11483, 0, [0,0,1,-112,456]]; ell_11731A = ["11731A", 11731, 0, [1,0,1,0,5]]; ell_11789A = ["11789A", 11789, 0, [1,1,1,-7,-8]]; ell_11867A = ["11867A", 11867, 0, [0,-1,1,4,-6]]; ell_11909A = ["11909A", 11909, 0, [0,1,1,-10,8]]; ell_11923A = ["11923A", 11923, 0, [0,1,1,-59,156]]; ell_11939A = ["11939A", 11939, 0, [0,-1,1,-57,186]]; ell_11939B = ["11939B", 11939, 0, [0,-1,1,6,-3]]; ell_11939C = ["11939C", 11939, 0, [0,-1,1,4,3]]; ell_11971A = ["11971A", 11971, 0, [0,0,1,1,5]]; ell_12007A = ["12007A", 12007, 0, [1,1,0,-6,1]]; ell_12011A = ["12011A", 12011, 0, [0,-1,1,-9,15]]; ell_12097A = ["12097A", 12097, 0, [1,-1,1,5,-4]]; ell_12101A = ["12101A", 12101, 0, [1,1,0,-12,-23]]; ell_12163A = ["12163A", 12163, 0, [0,-1,1,-10,17]]; ell_12163B = ["12163B", 12163, 0, [0,1,1,-53,-168]]; ell_12163C = ["12163C", 12163, 0, [1,1,1,-4,-8]]; ell_12197A = ["12197A", 12197, 0, [1,0,0,-24,43]]; ell_12203A = ["12203A", 12203, 0, [1,-1,0,-521,4710]]; ell_12203B = ["12203B", 12203, 0, [0,-1,1,-230,1422]]; ell_12211A = ["12211A", 12211, 0, [0,-1,1,-2,-5]]; ell_12227A = ["12227A", 12227, 0, [1,1,0,-365,-2842]]; ell_12277A = ["12277A", 12277, 0, [1,-1,1,2,-6]]; ell_12289A = ["12289A", 12289, 0, [1,0,0,-81,274]]; ell_12413A = ["12413A", 12413, 0, [1,1,0,-6,-11]]; ell_12547A = ["12547A", 12547, 0, [1,-1,0,-2,-5]]; ell_12553A = ["12553A", 12553, 0, [1,1,0,-1,-6]]; ell_12619A = ["12619A", 12619, 0, [0,-1,1,-6,10]]; ell_12619B = ["12619B", 12619, 0, [0,0,1,-8,10]]; ell_12619C = ["12619C", 12619, 0, [1,-1,1,-811,-8682]]; ell_12763A = ["12763A", 12763, 0, [1,-1,1,-7,10]]; ell_13043A = ["13043A", 13043, 0, [0,-1,1,1,-6]]; ell_13043B = ["13043B", 13043, 0, [1,0,1,-35,-81]]; ell_13093A = ["13093A", 13093, 0, [1,0,0,-8,-11]]; ell_13099A = ["13099A", 13099, 0, [1,0,1,-70,217]]; ell_13451A = ["13451A", 13451, 0, [1,0,0,5,4]]; ell_13523A = ["13523A", 13523, 0, [0,-1,1,-68,-195]]; ell_13523B = ["13523B", 13523, 0, [1,0,0,-33,-76]]; ell_13537A = ["13537A", 13537, 0, [1,-1,1,-19,36]]; ell_13619A = ["13619A", 13619, 0, [1,1,1,-47,-144]]; ell_13649A = ["13649A", 13649, 0, [1,1,1,-7,6]]; ell_13691A = ["13691A", 13691, 0, [0,-1,1,6,0]]; ell_13723A = ["13723A", 13723, 0, [1,1,1,-10481,408636]]; ell_13723B = ["13723B", 13723, 0, [1,1,1,6,2]]; ell_13789A = ["13789A", 13789, 0, [1,0,0,6,1]]; ell_14107A = ["14107A", 14107, 0, [0,-1,1,-3,7]]; ell_14149A = ["14149A", 14149, 0, [0,0,1,-7,4]]; ell_14173A = ["14173A", 14173, 0, [0,-1,1,-13,22]]; ell_14347A = ["14347A", 14347, 0, [0,0,1,1,-6]]; ell_14389A = ["14389A", 14389, 0, [1,1,1,-22,30]]; ell_14411A = ["14411A", 14411, 0, [0,-1,1,-62,210]]; ell_14461A = ["14461A", 14461, 0, [1,1,1,5,-2]]; ell_14821A = ["14821A", 14821, 0, [0,-1,1,-6,0]]; ell_14891A = ["14891A", 14891, 0, [1,0,0,-122,-529]]; ell_14957A = ["14957A", 14957, 0, [0,0,1,-11,-13]]; ell_15013A = ["15013A", 15013, 0, [0,0,1,-25,-48]]; ell_15083A = ["15083A", 15083, 0, [0,1,1,-34,66]]; ell_15091A = ["15091A", 15091, 0, [0,-1,1,6,-5]]; ell_15101A = ["15101A", 15101, 0, [0,0,1,-401,-3091]]; ell_15131A = ["15131A", 15131, 0, [0,1,1,3,-5]]; ell_15173A = ["15173A", 15173, 0, [1,1,1,5,6]]; ell_15193A = ["15193A", 15193, 0, [1,-1,0,-311,-2158]]; ell_15193B = ["15193B", 15193, 0, [1,0,0,-13,16]]; ell_15227A = ["15227A", 15227, 0, [0,1,1,-13,15]]; ell_15349A = ["15349A", 15349, 0, [1,1,0,-6,-5]]; ell_15391A = ["15391A", 15391, 0, [1,1,0,6,-1]]; ell_15551A = ["15551A", 15551, 0, [1,-1,0,-76,-237]]; ell_15619A = ["15619A", 15619, 0, [0,1,1,1,-6]]; ell_15641A = ["15641A", 15641, 0, [1,0,1,-12,15]]; ell_15641B = ["15641B", 15641, 0, [1,0,1,-7,-3]]; ell_15641C = ["15641C", 15641, 0, [1,-1,1,-106,-392]]; ell_15641D = ["15641D", 15641, 0, [1,0,0,-5116,-141273]]; ell_15643A = ["15643A", 15643, 0, [1,-1,0,-25,-42]]; ell_15661A = ["15661A", 15661, 0, [0,-1,1,-669,6888]]; ell_15661B = ["15661B", 15661, 0, [0,-1,1,-9,12]]; ell_15661C = ["15661C", 15661, 0, [0,-1,1,-6,3]]; ell_15661D = ["15661D", 15661, 0, [0,-1,1,-32,81]]; ell_15773A = ["15773A", 15773, 0, [1,0,0,-23,-44]]; ell_15803A = ["15803A", 15803, 0, [0,0,1,5,4]]; ell_15859A = ["15859A", 15859, 0, [1,-1,1,-741,-7574]]; ell_15877A = ["15877A", 15877, 0, [0,0,1,-7,-4]]; ell_15889A = ["15889A", 15889, 0, [1,1,1,-9,-16]]; ell_15971A = ["15971A", 15971, 0, [0,-1,1,-10,-11]]; ell_15973A = ["15973A", 15973, 0, [0,-1,1,-33,-63]]; ell_16057A = ["16057A", 16057, 0, [1,0,0,-13,18]]; ell_16061A = ["16061A", 16061, 0, [0,1,1,-6,-3]]; ell_16189A = ["16189A", 16189, 0, [1,0,0,-37,-90]]; ell_16193A = ["16193A", 16193, 0, [1,1,1,-332,-2594]]; ell_16267A = ["16267A", 16267, 0, [0,-1,1,4,4]]; ell_16363A = ["16363A", 16363, 0, [0,0,1,-2,6]]; ell_16369A = ["16369A", 16369, 0, [1,1,1,-12,-20]]; ell_16411A = ["16411A", 16411, 0, [1,1,0,-4,-9]]; ell_16487A = ["16487A", 16487, 0, [1,-1,1,-3,-6]]; ell_16649A = ["16649A", 16649, 0, [1,-1,0,-194,-993]]; ell_16649B = ["16649B", 16649, 0, [1,-1,0,-806,-8609]]; ell_16741A = ["16741A", 16741, 0, [1,-1,0,1,6]]; ell_16811A = ["16811A", 16811, 0, [0,0,1,-1,6]]; ell_16829A = ["16829A", 16829, 0, [1,1,1,1,-6]]; ell_16883A = ["16883A", 16883, 0, [0,1,1,-203,-1184]]; ell_16883B = ["16883B", 16883, 0, [0,1,1,-3,-8]]; ell_16883C = ["16883C", 16883, 0, [1,-1,1,-195,1094]]; ell_16889A = ["16889A", 16889, 0, [1,0,1,-89,313]]; ell_16937A = ["16937A", 16937, 0, [1,-1,0,-1,-6]]; ell_16963A = ["16963A", 16963, 0, [0,1,1,-178,857]]; ell_16987A = ["16987A", 16987, 0, [1,0,1,-62,-191]]; ell_17093A = ["17093A", 17093, 0, [0,1,1,-7,-7]]; ell_17093B = ["17093B", 17093, 0, [1,0,1,4,-5]]; ell_17299A = ["17299A", 17299, 0, [1,-1,1,-87,332]]; ell_17299B = ["17299B", 17299, 0, [0,1,1,-11,12]]; ell_17317A = ["17317A", 17317, 0, [1,-1,1,-145,-634]]; ell_17333A = ["17333A", 17333, 0, [0,-1,1,-196,1124]]; ell_17387A = ["17387A", 17387, 0, [0,0,1,2,6]]; ell_17387B = ["17387B", 17387, 0, [0,-1,1,-2,-6]]; ell_17387C = ["17387C", 17387, 0, [1,-1,1,0,6]]; ell_17389A = ["17389A", 17389, 0, [0,0,1,-7,3]]; ell_17443A = ["17443A", 17443, 0, [1,-1,0,-8,-9]]; ell_17483A = ["17483A", 17483, 0, [0,1,1,6,-2]]; ell_17491A = ["17491A", 17491, 0, [0,-1,1,-2,7]]; ell_17573A = ["17573A", 17573, 0, [0,-1,1,-42,-92]]; ell_17627A = ["17627A", 17627, 0, [1,0,1,-619,5869]]; ell_17681A = ["17681A", 17681, 0, [1,0,1,-17,25]]; ell_17747A = ["17747A", 17747, 0, [0,0,1,5,-5]]; ell_17747B = ["17747B", 17747, 0, [0,-1,1,-3,-6]]; ell_17747C = ["17747C", 17747, 0, [1,-1,1,-15,26]]; ell_17827A = ["17827A", 17827, 0, [0,-1,1,-17,34]]; ell_17837A = ["17837A", 17837, 0, [0,-1,1,-48,145]]; ell_17989A = ["17989A", 17989, 0, [1,1,1,-7,0]]; ell_18059A = ["18059A", 18059, 0, [0,-1,1,-47,141]]; ell_18059B = ["18059B", 18059, 0, [1,1,0,7,4]]; ell_18097A = ["18097A", 18097, 0, [1,1,1,-54,130]]; ell_18097B = ["18097B", 18097, 0, [1,1,1,-10,6]]; ell_18127A = ["18127A", 18127, 0, [1,0,1,6,-1]]; ell_18127B = ["18127B", 18127, 0, [1,1,0,-44,-133]]; ell_18149A = ["18149A", 18149, 0, [0,1,1,-17,-33]]; ell_18251A = ["18251A", 18251, 0, [0,1,1,-10,-18]]; ell_18251B = ["18251B", 18251, 0, [1,0,0,-40,-101]]; ell_18269A = ["18269A", 18269, 0, [1,-1,1,-19,-26]]; ell_18287A = ["18287A", 18287, 0, [1,-1,1,-7,0]]; ell_18289A = ["18289A", 18289, 0, [1,-1,1,-376,-2844]]; ell_18341A = ["18341A", 18341, 0, [1,-1,0,-28,65]]; ell_18379A = ["18379A", 18379, 0, [0,0,1,4,-6]]; ell_18397A = ["18397A", 18397, 0, [0,0,1,-181,937]]; ell_18397B = ["18397B", 18397, 0, [0,-1,1,-9,-6]]; ell_18523A = ["18523A", 18523, 0, [1,1,1,-7,-6]]; ell_18731A = ["18731A", 18731, 0, [0,1,1,-124,492]]; ell_18859A = ["18859A", 18859, 0, [0,-1,1,-22,-34]]; ell_18899A = ["18899A", 18899, 0, [1,-1,0,5,4]]; ell_19079A = ["19079A", 19079, 0, [1,0,0,-4,7]]; ell_19081A = ["19081A", 19081, 0, [1,-1,1,-7,-8]]; ell_19211A = ["19211A", 19211, 0, [1,0,1,-5,7]]; ell_19387A = ["19387A", 19387, 0, [0,1,1,7,3]]; ell_19387B = ["19387B", 19387, 0, [0,1,1,-363,-2787]]; ell_19403A = ["19403A", 19403, 0, [0,1,1,7,1]]; ell_19469A = ["19469A", 19469, 0, [1,0,0,-82,279]]; ell_19583A = ["19583A", 19583, 0, [1,1,1,2,-6]]; ell_19759A = ["19759A", 19759, 0, [1,0,0,-10,-11]]; ell_19927A = ["19927A", 19927, 0, [1,0,1,0,-7]]; /*************************************************************************/