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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 8712.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8712.p1 | 8712x1 | \([0, 0, 0, 243573, -17012842]\) | \(9987164/6561\) | \(-1049878407882433536\) | \([]\) | \(67584\) | \(2.1468\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8712.p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 8712.p do not have complex multiplication.Modular form 8712.2.a.p
sage: E.q_eigenform(10)