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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 493680.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 493680.h1 | 493680h1 | \([0, -1, 0, -177992976, -2479085734464]\) | \(-85944135790429956649/316171526414008320\) | \(-2294239827990638564915281920\) | \([]\) | \(211507200\) | \(3.9358\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 493680.h1 has rank \(0\).
Complex multiplication
The elliptic curves in class 493680.h do not have complex multiplication.Modular form 493680.2.a.h
sage: E.q_eigenform(10)