\\e0 is E:y^2=x^3+1 in char zero

{
e0=ellinit([0,0,0,0,1])
}
\\ p is the generic point on e0
{
p=[t,Mod(x,x^2-t^3-1)]
}
\\ f is f_5 whose roots are the x-coords of 5-torsion pts. 
\\ The "simplify" defies explanation goes around some bug in pari
{
f=factor(denominator(simplify(ellpow(e0,p,5)[1])))[1,1]
}
\\a is a root of f in F_{7^12}
{
a=Mod(Mod(1, 7)*t,Mod(1, 7)*f) 
}
\\v is a square root of a^3+1 in F_{7^24}
{
v=Mod(Mod(1, 7)*x, 
Mod(1, 7)*x^2 + Mod(Mod(6, 7)*t^3 + Mod(6, 7), 
Mod(1, 7)*t^12 + Mod(6, 7)*t^9 + Mod(1, 7)*t^6 + Mod(2, 7)*t^3 + Mod(2, 7)))
}
\\ q is a 5-torsion point in E mod 7
{
q=[a,v]
}
\\E in char 7
{
e=ellinit(Mod(1,7)*[0,0,0,0,1])
}
\\ Frobenius of q
{
qq=[a^7,v^7]
}
\\ Frobenius of qq
{
qqq=[a^49,v^49]
}
\\ qqq + 2q in E mod 7
{
rhs=elladd(e,qqq,ellpow(e,q,2))
}
\\ finds m for which rhs = m*qq on E
{
for(m=1,4,if(rhs-ellpow(e,qq,m)==[0,0],print(m" is t modulo 5")))
}