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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 41405.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41405.g1 | 41405c1 | \([1, -1, 1, 39852, 36750172]\) | \(251559/21125\) | \(-587815659518940125\) | \([]\) | \(846720\) | \(2.0891\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41405.g1 has rank \(1\).
Complex multiplication
The elliptic curves in class 41405.g do not have complex multiplication.Modular form 41405.2.a.g
sage: E.q_eigenform(10)