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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 360789.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 360789.h1 | 360789h1 | \([0, -1, 1, -75914827, -813000367071]\) | \(-115006810390528/612198951507\) | \(-257556527117793887572352907\) | \([]\) | \(112696320\) | \(3.7519\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 360789.h1 has rank \(1\).
Complex multiplication
The elliptic curves in class 360789.h do not have complex multiplication.Modular form 360789.2.a.h
sage: E.q_eigenform(10)