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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 169065.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169065.f1 | 169065b1 | \([0, 0, 1, -495057, -137670858]\) | \(-762549907456/24024195\) | \(-422736649407345195\) | \([]\) | \(3472896\) | \(2.1585\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 169065.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 169065.f do not have complex multiplication.Modular form 169065.2.a.f
sage: E.q_eigenform(10)