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SageMath
E = EllipticCurve("hp1")
E.isogeny_class()
Elliptic curves in class 162624hp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162624.bx1 | 162624hp1 | \([0, -1, 0, -803601, -286913031]\) | \(-31636584484096/1331669031\) | \(-2415752110312848384\) | \([]\) | \(2764800\) | \(2.2940\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 162624hp1 has rank \(1\).
Complex multiplication
The elliptic curves in class 162624hp do not have complex multiplication.Modular form 162624.2.a.hp
sage: E.q_eigenform(10)