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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 465690f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
465690.f1 | 465690f1 | \([1, 1, 0, -704318, -229847628]\) | \(-821314391438449/8576539200\) | \(-403490842595035200\) | \([]\) | \(8294400\) | \(2.1955\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 465690f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 465690f do not have complex multiplication.Modular form 465690.2.a.f
sage: E.q_eigenform(10)