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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 229320.cp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
229320.cp1 | 229320b1 | \([0, 0, 0, -2837982, 1840484149]\) | \(-767228471296/142155\) | \(-468371057867884080\) | \([]\) | \(4440576\) | \(2.3931\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 229320.cp1 has rank \(1\).
Complex multiplication
The elliptic curves in class 229320.cp do not have complex multiplication.Modular form 229320.2.a.cp
sage: E.q_eigenform(10)