Step 1: The lattice Λf
Recall that Ef = C/Λf with Λf = {
R
γ
ωf : γ ∈ H1(X1(N), Z)}. The map
Γ1(N) → H1(X1(N), Z), g 7→ {0, g0}
is a surjective group morphism.
1. Compute generators g1, . . . , gr of Γ1(N) (more generally, ΓH (N))
using msfarey and mspolygon.
2. For each 1 ≤ i ≤ r, compute I(gi ) =
R gi 0
0
ωf using mfsymboleval.
3. Compute Z-generators of Λf = hI(g1), . . . , I(gr )i using lindep and
qflll.
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