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SageMath
E = EllipticCurve("hp1")
E.isogeny_class()
Elliptic curves in class 426888.hp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 426888.hp1 | 426888hp1 | \([0, 0, 0, 189189, 30255687]\) | \(15185664/16807\) | \(-828834405727459824\) | \([]\) | \(7741440\) | \(2.1247\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 426888.hp1 has rank \(0\).
Complex multiplication
The elliptic curves in class 426888.hp do not have complex multiplication.Modular form 426888.2.a.hp
sage: E.q_eigenform(10)