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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 162624.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162624.z1 | 162624ch1 | \([0, -1, 0, 420406111, 8186239337025]\) | \(146234339790153527/599838494072832\) | \(-33706661214991784351102926848\) | \([]\) | \(138378240\) | \(4.1566\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 162624.z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 162624.z do not have complex multiplication.Modular form 162624.2.a.z
sage: E.q_eigenform(10)