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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 76440b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76440.f1 | 76440b1 | \([0, -1, 0, -1538616, 738962316]\) | \(-81920503901854898/499763671875\) | \(-2457461916000000000\) | \([]\) | \(1866240\) | \(2.3679\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 76440b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 76440b do not have complex multiplication.Modular form 76440.2.a.b
sage: E.q_eigenform(10)