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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 123210.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123210.f1 | 123210c1 | \([1, -1, 0, 141435, 7415381]\) | \(4516672077/2960000\) | \(-205052854607280000\) | \([]\) | \(1225728\) | \(2.0107\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 123210.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 123210.f do not have complex multiplication.Modular form 123210.2.a.f
sage: E.q_eigenform(10)