Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("13520.bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13520.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
13520.bc1 13520bb3 [0, -1, 0, -6985, 226992] [2] 13824  
13520.bc2 13520bb4 [0, -1, 0, -6140, 283100] [2] 27648  
13520.bc3 13520bb1 [0, -1, 0, -225, -820] [2] 4608 \(\Gamma_0(N)\)-optimal
13520.bc4 13520bb2 [0, -1, 0, 620, -6228] [2] 9216  

Rank

sage: E.rank()
 

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

Modular form 13520.2.a.bc

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

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 LMFDB 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 LMFDB labels.