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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 319725.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
319725.f1 | 319725f1 | \([0, 0, 1, -3178875, 2385082656]\) | \(-106039644160/11986947\) | \(-401591385477573046875\) | \([]\) | \(15667200\) | \(2.6904\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 319725.f1 has rank \(2\).
Complex multiplication
The elliptic curves in class 319725.f do not have complex multiplication.Modular form 319725.2.a.f
sage: E.q_eigenform(10)