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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 64400.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64400.ca1 | 64400s1 | \([0, 1, 0, -708, -7537]\) | \(-157216000/1127\) | \(-281750000\) | \([]\) | \(27648\) | \(0.45381\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 64400.ca1 has rank \(1\).
Complex multiplication
The elliptic curves in class 64400.ca do not have complex multiplication.Modular form 64400.2.a.ca
sage: E.q_eigenform(10)