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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 266616.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 266616.bc1 | 266616bc1 | \([0, 0, 0, 116287425, -12225692719809]\) | \(100718081964000000/37453512751940327\) | \(-64670628753923348933863479792\) | \([]\) | \(180956160\) | \(4.2074\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 266616.bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 266616.bc do not have complex multiplication.Modular form 266616.2.a.bc
sage: E.q_eigenform(10)