Properties

Label 26743.b
Number of curves $1$
Conductor $26743$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 26743.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26743.b1 26743b1 \([1, 1, 1, -1423, 20548]\) \(-318681965472625/8658340423\) \(-8658340423\) \([]\) \(13584\) \(0.68833\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 26743.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 26743.b do not have complex multiplication.

Modular form 26743.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} - q^{4} - 2 q^{6} + q^{7} + 3 q^{8} + q^{9} + 3 q^{11} - 2 q^{12} - q^{14} - q^{16} - 3 q^{17} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display