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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 311696z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
311696.z1 | 311696z1 | \([0, -1, 0, -1335880, -573886432]\) | \(109192361324/4173281\) | \(10076547376992431104\) | \([]\) | \(4257792\) | \(2.4144\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 311696z1 has rank \(2\).
Complex multiplication
The elliptic curves in class 311696z do not have complex multiplication.Modular form 311696.2.a.z
sage: E.q_eigenform(10)