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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 189618.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 189618.h1 | 189618bp1 | \([1, 1, 0, 193333, -23298004803]\) | \(165568631260031/48580832601759744\) | \(-234490400029667348176896\) | \([]\) | \(21525504\) | \(3.1632\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 189618.h1 has rank \(0\).
Complex multiplication
The elliptic curves in class 189618.h do not have complex multiplication.Modular form 189618.2.a.h
sage: E.q_eigenform(10)