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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 429429i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
429429.i1 | 429429i1 | \([0, -1, 1, -6468700, -44781613680]\) | \(-1593413632/45196767\) | \(-849089854809530742459051\) | \([]\) | \(97044480\) | \(3.2720\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 429429i1 has rank \(2\).
Complex multiplication
The elliptic curves in class 429429i do not have complex multiplication.Modular form 429429.2.a.i
sage: E.q_eigenform(10)