Properties

Label 13200.cu
Number of curves 4
Conductor 13200
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("13200.cu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13200.cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
13200.cu1 13200bb3 [0, 1, 0, -17608, -905212] [2] 24576  
13200.cu2 13200bb4 [0, 1, 0, -2608, 30788] [2] 24576  
13200.cu3 13200bb2 [0, 1, 0, -1108, -14212] [2, 2] 12288  
13200.cu4 13200bb1 [0, 1, 0, 17, -712] [2] 6144 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 13200.cu have rank \(1\).

Modular form 13200.2.a.cu

sage: E.q_eigenform(10)
 
\( q + q^{3} + 4q^{7} + q^{9} + q^{11} - 6q^{13} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.