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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 455175du
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
455175.du1 | 455175du1 | \([1, -1, 0, -129303567, 565963998466]\) | \(-72628961394279272329/24608375505\) | \(-81008080621389140625\) | \([]\) | \(38568960\) | \(3.1772\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 455175du1 has rank \(0\).
Complex multiplication
The elliptic curves in class 455175du do not have complex multiplication.Modular form 455175.2.a.du
sage: E.q_eigenform(10)