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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 257400a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257400.a1 | 257400a1 | \([0, 0, 0, 2625, 31475]\) | \(274400000/217503\) | \(-1585596870000\) | \([]\) | \(516096\) | \(1.0289\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257400a1 has rank \(2\).
Complex multiplication
The elliptic curves in class 257400a do not have complex multiplication.Modular form 257400.2.a.a
sage: E.q_eigenform(10)