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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 257400x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257400.x1 | 257400x1 | \([0, 0, 0, 9825, 44575]\) | \(14387782400/8444007\) | \(-61556811030000\) | \([]\) | \(706560\) | \(1.3353\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257400x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 257400x do not have complex multiplication.Modular form 257400.2.a.x
sage: E.q_eigenform(10)