Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 257400v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257400.v1 | 257400v1 | \([0, 0, 0, -45255675, 117196501750]\) | \(-439405355845493858/66715782705\) | \(-1556345778942240000000\) | \([]\) | \(17141760\) | \(3.0790\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257400v1 has rank \(1\).
Complex multiplication
The elliptic curves in class 257400v do not have complex multiplication.Modular form 257400.2.a.v
sage: E.q_eigenform(10)