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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 574.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
574.f1 | 574e1 | \([1, -1, 0, -40, -88]\) | \(7177888089/2296\) | \(2296\) | \([]\) | \(120\) | \(-0.38029\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 574.f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 574.f do not have complex multiplication.Modular form 574.2.a.f
sage: E.q_eigenform(10)