Step 2: The elliptic curve Ef
The elliptic curve Ef = C/Λf has Weierstrass equation
Ef : y2
= x3
− 27c4(Λf )x − 54c6(Λf ).
Hypothesis: c4(Λf ), c6(Λf ) ∈ Q(ζN ).
(This does not always hold.)
1. Compute c4, c6 as complex numbers.
2. Reconstruct c4, c6 in Q(ζN ) using lindep.
We will see later how to check the Weierstrass equation is correct.
8