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SageMath
E = EllipticCurve("gm1")
E.isogeny_class()
Elliptic curves in class 458640gm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
458640.gm1 | 458640gm1 | \([0, 0, 0, -957243, -2214635542]\) | \(-662989657192009/14097531093750\) | \(-2062655111986560000000\) | \([]\) | \(25804800\) | \(2.7707\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 458640gm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 458640gm do not have complex multiplication.Modular form 458640.2.a.gm
sage: E.q_eigenform(10)