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SageMath
E = EllipticCurve("hp1")
E.isogeny_class()
Elliptic curves in class 474320.hp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 474320.hp1 | 474320hp1 | \([0, 1, 0, -96840, 77848868]\) | \(-196/5\) | \(-2562161329119687680\) | \([]\) | \(5644800\) | \(2.2129\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 474320.hp1 has rank \(0\).
Complex multiplication
The elliptic curves in class 474320.hp do not have complex multiplication.Modular form 474320.2.a.hp
sage: E.q_eigenform(10)