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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 166635ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
166635.bz1 | 166635ca1 | \([0, 0, 1, -42573, -3245697]\) | \(22128056725504/1004653125\) | \(387435435778125\) | \([]\) | \(1228800\) | \(1.5613\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 166635ca1 has rank \(1\).
Complex multiplication
The elliptic curves in class 166635ca do not have complex multiplication.Modular form 166635.2.a.ca
sage: E.q_eigenform(10)