p-adic strategy to compute ρJ,`
1 Choose prime p - ` of good reduction of C,
2 Find q = pa
such that J[`] is defined over Fq,
3 Generate random points of J(Fq)[`] until we get
an F`-basis,
4 Lift this basis from J(Fq) to J(Zq/pe
), e  1,
5 Form all linear combinations of these points
in J(Zq/pe
)[`],
6 F(x) =
Q
t∈J[`] x − θ(t)


, where θ : J 99K A1
,
7 Identify F(x) ∈ Q[x].
Nicolas Mascot p-adic computation of Galois representations