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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 81232b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 81232.b1 | 81232b1 | \([0, 1, 0, -2169, -39613]\) | \(4410243976192/5077\) | \(1299712\) | \([]\) | \(23808\) | \(0.45719\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 81232b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 81232b do not have complex multiplication.Modular form 81232.2.a.b
sage: E.q_eigenform(10)