Properties

Label 23232t
Number of curves 2
Conductor 23232
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("23232.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23232t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23232.n2 23232t1 [0, -1, 0, 1291, 9429] [2] 23040 \(\Gamma_0(N)\)-optimal
23232.n1 23232t2 [0, -1, 0, -5969, 86385] [2] 46080  

Rank

sage: E.rank()
 

The elliptic curves in class 23232t have rank \(2\).

Modular form 23232.2.a.n

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.