Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("23232.dr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23232.dr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23232.dr1 23232dq4 [0, 1, 0, -340897, 76495967] [2] 184320  
23232.dr2 23232dq3 [0, 1, 0, -50497, -2713537] [2] 184320  
23232.dr3 23232dq2 [0, 1, 0, -21457, 1172015] [2, 2] 92160  
23232.dr4 23232dq1 [0, 1, 0, 323, 61235] [2] 46080 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 23232.2.a.dr

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{5} + 4q^{7} + q^{9} + 6q^{13} + 2q^{15} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.