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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 1785f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1785.g1 | 1785f1 | \([0, -1, 1, -35, 131]\) | \(-4878401536/3346875\) | \(-3346875\) | \([]\) | \(240\) | \(-0.047669\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1785f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1785f do not have complex multiplication.Modular form 1785.2.a.f
sage: E.q_eigenform(10)