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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 229320ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
229320.u1 | 229320ca1 | \([0, 0, 0, -1674183, 6586139882]\) | \(-482370434896/17138671875\) | \(-18438643938487500000000\) | \([]\) | \(12063744\) | \(2.9526\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 229320ca1 has rank \(1\).
Complex multiplication
The elliptic curves in class 229320ca do not have complex multiplication.Modular form 229320.2.a.ca
sage: E.q_eigenform(10)