Properties

Label 23232.dj
Number of curves 4
Conductor 23232
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("23232.dj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23232.dj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23232.dj1 23232ca4 [0, 1, 0, -1134657, -465127137] [2] 368640  
23232.dj2 23232ca2 [0, 1, 0, -89217, -3251745] [2, 2] 184320  
23232.dj3 23232ca1 [0, 1, 0, -50497, 4314143] [2] 92160 \(\Gamma_0(N)\)-optimal
23232.dj4 23232ca3 [0, 1, 0, 336703, -24973665] [2] 368640  

Rank

sage: E.rank()
 

The elliptic curves in class 23232.dj have rank \(1\).

Modular form 23232.2.a.dj

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.