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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 45177f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
45177.m1 | 45177f1 | \([0, 1, 1, 32770, -1699057]\) | \(2842734729383936/2567805035499\) | \(-3515325093598131\) | \([]\) | \(329472\) | \(1.6703\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 45177f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 45177f do not have complex multiplication.Modular form 45177.2.a.f
sage: E.q_eigenform(10)