Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("23232.bs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23232db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23232.bs3 23232db1 [0, -1, 0, -50497, -4314143] [2] 92160 \(\Gamma_0(N)\)-optimal
23232.bs2 23232db2 [0, -1, 0, -89217, 3251745] [2, 2] 184320  
23232.bs4 23232db3 [0, -1, 0, 336703, 24973665] [2] 368640  
23232.bs1 23232db4 [0, -1, 0, -1134657, 465127137] [2] 368640  

Rank

sage: E.rank()
 

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

Modular form 23232.2.a.bs

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.