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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 429429z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
429429.z1 | 429429z1 | \([1, 1, 1, -47282232, 521303305986]\) | \(-118436464005435433/1120962830293089\) | \(-110642861950071037885747449\) | \([]\) | \(94558464\) | \(3.6797\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 429429z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 429429z do not have complex multiplication.Modular form 429429.2.a.z
sage: E.q_eigenform(10)