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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 194579.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
194579.f1 | 194579f1 | \([0, 0, 1, 35378, 588159]\) | \(884736/539\) | \(-2983311560181491\) | \([]\) | \(1257984\) | \(1.6585\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 194579.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 194579.f do not have complex multiplication.Modular form 194579.2.a.f
sage: E.q_eigenform(10)