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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 257400f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257400.f1 | 257400f1 | \([0, 0, 0, -856432875, -24152451336250]\) | \(-119120411792671966610/363168950990295879\) | \(-211800132217540556632800000000\) | \([]\) | \(283852800\) | \(4.3138\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257400f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 257400f do not have complex multiplication.Modular form 257400.2.a.f
sage: E.q_eigenform(10)