Properties

Label 13200ck
Number of curves 4
Conductor 13200
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("13200.cp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13200ck

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
13200.cp3 13200ck1 [0, 1, 0, -2208, -38412] [2] 13824 \(\Gamma_0(N)\)-optimal
13200.cp4 13200ck2 [0, 1, 0, 1792, -158412] [2] 27648  
13200.cp1 13200ck3 [0, 1, 0, -32208, 2205588] [2] 41472  
13200.cp2 13200ck4 [0, 1, 0, -16208, 4413588] [2] 82944  

Rank

sage: E.rank()
 

The elliptic curves in class 13200ck have rank \(0\).

Modular form 13200.2.a.cp

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{7} + q^{9} + q^{11} + 4q^{13} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.