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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 191100.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 191100.bg1 | 191100bt1 | \([0, -1, 0, -74251333, 250470805537]\) | \(-769623354048512/15247889631\) | \(-896949483598759500000000\) | \([]\) | \(27720000\) | \(3.3890\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 191100.bg1 has rank \(1\).
Complex multiplication
The elliptic curves in class 191100.bg do not have complex multiplication.Modular form 191100.2.a.bg
sage: E.q_eigenform(10)