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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 8640.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8640.ca1 | 8640cc1 | \([0, 0, 0, 1188, 32616]\) | \(1022208/3125\) | \(-566870400000\) | \([]\) | \(11520\) | \(0.93859\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8640.ca1 has rank \(0\).
Complex multiplication
The elliptic curves in class 8640.ca do not have complex multiplication.Modular form 8640.2.a.ca
sage: E.q_eigenform(10)