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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 86640.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86640.z1 | 86640cl1 | \([0, -1, 0, 3490, 178227]\) | \(2253933824/7971615\) | \(-16621901414640\) | \([]\) | \(168480\) | \(1.2198\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 86640.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 86640.z do not have complex multiplication.Modular form 86640.2.a.z
sage: E.q_eigenform(10)