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SageMath
E = EllipticCurve("hp1")
E.isogeny_class()
Elliptic curves in class 162624.hp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162624.hp1 | 162624ba1 | \([0, 1, 0, -645, 5091]\) | \(123904/21\) | \(5037441024\) | \([]\) | \(86016\) | \(0.58243\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 162624.hp1 has rank \(1\).
Complex multiplication
The elliptic curves in class 162624.hp do not have complex multiplication.Modular form 162624.2.a.hp
sage: E.q_eigenform(10)