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SageMath
sage: E = EllipticCurve("bc1")
sage: E.isogeny_class()
Elliptic curves in class 15680.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15680.bc1 | 15680cg1 | \([0, -1, 0, -3691, 87641]\) | \(-738763264/875\) | \(-6588344000\) | \([]\) | \(9216\) | \(0.79560\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 15680.bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 15680.bc do not have complex multiplication.Modular form 15680.2.a.bc
sage: E.q_eigenform(10)