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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 355740.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 355740.c1 | 355740c1 | \([0, -1, 0, -11645773421, 483952469279721]\) | \(-3273741656681120014336/1733575611796875\) | \(-92496884499186942339180000000\) | \([]\) | \(522547200\) | \(4.5080\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 355740.c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 355740.c do not have complex multiplication.Modular form 355740.2.a.c
sage: E.q_eigenform(10)