Properties

Label 11760.cl
Number of curves $8$
Conductor $11760$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("11760.cl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11760.cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.cl1 11760co7 [0, 1, 0, -5057600, 2752600500] [2] 663552  
11760.cl2 11760co4 [0, 1, 0, -4516640, 3693127668] [2] 221184  
11760.cl3 11760co6 [0, 1, 0, -2117600, -1155247500] [2, 2] 331776  
11760.cl4 11760co3 [0, 1, 0, -2101920, -1173630732] [2] 165888  
11760.cl5 11760co2 [0, 1, 0, -283040, 57311988] [2, 2] 110592  
11760.cl6 11760co5 [0, 1, 0, -63520, 144154100] [4] 221184  
11760.cl7 11760co1 [0, 1, 0, -32160, -791820] [2] 55296 \(\Gamma_0(N)\)-optimal
11760.cl8 11760co8 [0, 1, 0, 571520, -3886317772] [4] 663552  

Rank

sage: E.rank()
 

The elliptic curves in class 11760.cl have rank \(1\).

Modular form 11760.2.a.cl

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} + q^{9} - 2q^{13} + q^{15} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.