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SageMath
E = EllipticCurve("hp1")
E.isogeny_class()
Elliptic curves in class 176400hp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.gv1 | 176400hp1 | \([0, 0, 0, -6354075, -6237197750]\) | \(-105484561/1440\) | \(-387306079856640000000\) | \([]\) | \(7741440\) | \(2.7573\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 176400hp1 has rank \(1\).
Complex multiplication
The elliptic curves in class 176400hp do not have complex multiplication.Modular form 176400.2.a.hp
sage: E.q_eigenform(10)