Properties

Label 13520.l
Number of curves 4
Conductor 13520
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("13520.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13520.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
13520.l1 13520a3 [0, 0, 0, -18083, 935922] [2] 18432  
13520.l2 13520a2 [0, 0, 0, -1183, 13182] [2, 2] 9216  
13520.l3 13520a1 [0, 0, 0, -338, -2197] [2] 4608 \(\Gamma_0(N)\)-optimal
13520.l4 13520a4 [0, 0, 0, 2197, 74698] [2] 18432  

Rank

sage: E.rank()
 

The elliptic curves in class 13520.l have rank \(1\).

Modular form 13520.2.a.l

sage: E.q_eigenform(10)
 
\( q - q^{5} - 4q^{7} - 3q^{9} + 4q^{11} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.