Properties

Label 23232ca
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 23232ca

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
23232.dj3 23232ca1 [0, 1, 0, -50497, 4314143] 2 92160 \(\Gamma_0(N)\)-optimal
23232.dj2 23232ca2 [0, 1, 0, -89217, -3251745] 4 184320  
23232.dj4 23232ca3 [0, 1, 0, 336703, -24973665] 2 368640  
23232.dj1 23232ca4 [0, 1, 0, -1134657, -465127137] 2 368640  

Rank

sage: E.rank()

The elliptic curves in class 23232ca 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 Cremona 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 Cremona labels.