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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 12525b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12525.d1 | 12525b1 | \([1, 1, 0, -35575, 2576500]\) | \(-2549455723781/9861183\) | \(-19260123046875\) | \([]\) | \(46400\) | \(1.4075\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12525b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 12525b do not have complex multiplication.Modular form 12525.2.a.b
sage: E.q_eigenform(10)