Properties

Label 126.b
Number of curves 6
Conductor 126
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("126.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 126.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
126.b1 126a6 [1, -1, 1, -24575, 1488935] [6] 144  
126.b2 126a5 [1, -1, 1, -1535, 23591] [6] 72  
126.b3 126a4 [1, -1, 1, -320, 1883] [6] 48  
126.b4 126a2 [1, -1, 1, -95, -331] [2] 16  
126.b5 126a1 [1, -1, 1, -5, -7] [2] 8 \(\Gamma_0(N)\)-optimal
126.b6 126a3 [1, -1, 1, 40, 155] [6] 24  

Rank

sage: E.rank()
 

The elliptic curves in class 126.b have rank \(0\).

Modular form 126.2.a.b

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{7} + q^{8} - 4q^{13} + q^{14} + q^{16} - 6q^{17} + 2q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.