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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 488410h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 488410.h1 | 488410h1 | \([1, 1, 0, -193508, 32795872]\) | \(-574468255729/2284880\) | \(-3187288331548880\) | \([]\) | \(3290112\) | \(1.8320\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 488410h1 has rank \(1\).
Complex multiplication
The elliptic curves in class 488410h do not have complex multiplication.Modular form 488410.2.a.h
sage: E.q_eigenform(10)