Properties

Label 257754t
Number of curves $1$
Conductor $257754$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 257754t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257754.t1 257754t1 \([1, 0, 1, -15325584270, 4805543586792352]\) \(-23439374927166990900760633/573844026377336511607776\) \(-9745916197680761498561691961806816\) \([]\) \(2118758400\) \(5.2025\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257754t1 has rank \(0\).

Complex multiplication

The elliptic curves in class 257754t do not have complex multiplication.

Modular form 257754.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 3 q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + 3 q^{10} + 2 q^{11} + q^{12} + 3 q^{13} + q^{14} - 3 q^{15} + q^{16} - q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display