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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 405600z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405600.z1 | 405600z1 | \([0, -1, 0, -413768, -102734568]\) | \(-150061288/729\) | \(-38058732518976000\) | \([]\) | \(4432896\) | \(2.0301\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 405600z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 405600z do not have complex multiplication.Modular form 405600.2.a.z
sage: E.q_eigenform(10)