Properties

Label 257754h
Number of curves $1$
Conductor $257754$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 257754h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257754.h1 257754h1 \([1, 1, 0, 21292, 49446]\) \(62851031/36414\) \(-618439464574974\) \([]\) \(1488384\) \(1.5276\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257754h1 has rank \(1\).

Complex multiplication

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

Modular form 257754.2.a.h

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