Properties

Label 166175u
Number of curves $1$
Conductor $166175$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 166175u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166175.u1 166175u1 \([0, 1, 1, -132458, 18578619]\) \(-5451776/23\) \(-1084304857421875\) \([]\) \(1339520\) \(1.7396\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 166175u1 has rank \(1\).

Complex multiplication

The elliptic curves in class 166175u do not have complex multiplication.

Modular form 166175.2.a.u

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{6} - q^{7} + q^{9} - 4 q^{12} + 2 q^{13} - 2 q^{14} - 4 q^{16} + 2 q^{18} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display