Properties

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

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 257754y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257754.y1 257754y1 \([1, 0, 1, -451277, 120346184]\) \(-28154299464100934497/1049537371938048\) \(-378882991269635328\) \([]\) \(5529600\) \(2.1436\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257754y1 has rank \(2\).

Complex multiplication

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

Modular form 257754.2.a.y

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