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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 344760.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 344760.bc1 | 344760bc1 | \([0, -1, 0, -17978587800, 927909138287052]\) | \(-2276286710084294740898/128433112734375\) | \(-36261059020868677713120000000\) | \([]\) | \(553512960\) | \(4.5446\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 344760.bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 344760.bc do not have complex multiplication.Modular form 344760.2.a.bc
sage: E.q_eigenform(10)