Properties

Label 23232.cv
Number of curves 4
Conductor 23232
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("23232.cv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23232.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23232.cv1 23232dm3 [0, 1, 0, -623553, -189003201] [2] 276480  
23232.cv2 23232dm4 [0, 1, 0, -313793, -376531905] [2] 552960  
23232.cv3 23232dm1 [0, 1, 0, -42753, 3195135] [2] 92160 \(\Gamma_0(N)\)-optimal
23232.cv4 23232dm2 [0, 1, 0, 34687, 13556607] [2] 184320  

Rank

sage: E.rank()
 

The elliptic curves in class 23232.cv have rank \(0\).

Modular form 23232.2.a.cv

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{7} + q^{9} - 4q^{13} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.