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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 2166.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2166.f1 | 2166g1 | \([1, 1, 1, 31580, -2764459]\) | \(205083359/314928\) | \(-5348599541376048\) | \([]\) | \(24624\) | \(1.7033\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 2166.f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 2166.f do not have complex multiplication.Modular form 2166.2.a.f
sage: E.q_eigenform(10)