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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 20808bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20808.t1 | 20808bc1 | \([0, 0, 0, -2505630, 3460191509]\) | \(-73984000/177147\) | \(-4165532494575834130992\) | \([]\) | \(1077120\) | \(2.8366\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 20808bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 20808bc do not have complex multiplication.Modular form 20808.2.a.bc
sage: E.q_eigenform(10)