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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 288834.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 288834.bc1 | 288834bc1 | \([1, 1, 1, -53156047, 149999668565]\) | \(-112205650221491190337/745029571313664\) | \(-110291114920707148087296\) | \([]\) | \(55187440\) | \(3.2570\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 288834.bc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 288834.bc do not have complex multiplication.Modular form 288834.2.a.bc
sage: E.q_eigenform(10)