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SageMath
E = EllipticCurve("ph1")
E.isogeny_class()
Elliptic curves in class 310464ph
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.ph1 | 310464ph1 | \([0, 0, 0, -765736524, 8157942738288]\) | \(-34068278205171/10307264\) | \(-15022942823461329485955072\) | \([]\) | \(81285120\) | \(3.8086\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 310464ph1 has rank \(1\).
Complex multiplication
The elliptic curves in class 310464ph do not have complex multiplication.Modular form 310464.2.a.ph
sage: E.q_eigenform(10)