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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 489762.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
489762.f1 | 489762f1 | \([1, -1, 0, 14389389, -31354986519]\) | \(3278609582807/6122436516\) | \(-615297771247477343443236\) | \([]\) | \(77475840\) | \(3.2494\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 489762.f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 489762.f do not have complex multiplication.Modular form 489762.2.a.f
sage: E.q_eigenform(10)