Properties

Label 455175du
Number of curves $1$
Conductor $455175$
CM no
Rank $0$

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Show commands: 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)
 
\(q + q^{2} - q^{4} - q^{7} - 3 q^{8} - q^{11} + q^{13} - q^{14} - q^{16} + O(q^{20})\) Copy content Toggle raw display