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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 12600.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12600.bc1 | 12600p1 | \([0, 0, 0, -92700, -11191500]\) | \(-30211716096/1071875\) | \(-3125587500000000\) | \([]\) | \(80640\) | \(1.7455\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12600.bc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 12600.bc do not have complex multiplication.Modular form 12600.2.a.bc
sage: E.q_eigenform(10)