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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 128576ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
128576.bc1 | 128576ca1 | \([0, -1, 0, -2025, -34271]\) | \(373698304/1681\) | \(4132946944\) | \([]\) | \(78336\) | \(0.69682\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 128576ca1 has rank \(0\).
Complex multiplication
The elliptic curves in class 128576ca do not have complex multiplication.Modular form 128576.2.a.ca
sage: E.q_eigenform(10)