Properties

Label 5746.b
Number of curves 4
Conductor 5746
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("5746.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5746.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5746.b1 5746e4 [1, 0, 1, -19101, -703714] [2] 27648  
5746.b2 5746e3 [1, 0, 1, -17411, -885558] [2] 13824  
5746.b3 5746e2 [1, 0, 1, -7271, 237954] [2] 9216  
5746.b4 5746e1 [1, 0, 1, -511, 2706] [2] 4608 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5746.b have rank \(1\).

Modular form 5746.2.a.b

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.