Properties

Label 257754s
Number of curves $1$
Conductor $257754$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 257754s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257754.s1 257754s1 \([1, 0, 1, 277, -538]\) \(6544969919/4164048\) \(-1503221328\) \([]\) \(258048\) \(0.44989\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257754s1 has rank \(2\).

Complex multiplication

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

Modular form 257754.2.a.s

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