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SageMath
E = EllipticCurve("ho1")
E.isogeny_class()
Elliptic curves in class 284592ho
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 284592.ho1 | 284592ho1 | \([0, 1, 0, -12756, -605277]\) | \(-91625216/9261\) | \(-23203001196144\) | \([]\) | \(663552\) | \(1.3046\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 284592ho1 has rank \(1\).
Complex multiplication
The elliptic curves in class 284592ho do not have complex multiplication.Modular form 284592.2.a.ho
sage: E.q_eigenform(10)