Example: 2-torsion of the Klein quartic
Let C : x3
y + y3
+ x = 0. We compute ρJ,2.
f = x^3*y+y^3+x;
P = [1,0,0]; \\ Points on C
Q = [0,1,0]; \\ Needed to construct J -> A1
l = 2; \\ Look at J[2]
p = 5; e = 60; \\ Work mod 5^60
R = smoothplanegalrep(f,l,p,e,[[P],[Q]])
fa = factor(R[1])
Mat(apply(polredabs,fa[,1]))
We see that the field of definition of J[2] is Q(ζ7).
Nicolas Mascot p-adic computation of Galois representations