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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 139425.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139425.z1 | 139425x1 | \([0, 1, 1, 2817, -7081]\) | \(5537792/3267\) | \(-1457949796875\) | \([]\) | \(165888\) | \(1.0234\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 139425.z1 has rank \(2\).
Complex multiplication
The elliptic curves in class 139425.z do not have complex multiplication.Modular form 139425.2.a.z
sage: E.q_eigenform(10)