Properties

Label 2366.j
Number of curves 6
Conductor 2366
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("2366.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2366.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2366.j1 2366j6 [1, 0, 0, -461458, -120693756] [2] 12960  
2366.j2 2366j5 [1, 0, 0, -28818, -1890812] [2] 6480  
2366.j3 2366j4 [1, 0, 0, -6003, -147239] [2] 4320  
2366.j4 2366j2 [1, 0, 0, -1778, 28690] [2] 1440  
2366.j5 2366j1 [1, 0, 0, -88, 636] [2] 720 \(\Gamma_0(N)\)-optimal
2366.j6 2366j3 [1, 0, 0, 757, -13391] [2] 2160  

Rank

sage: E.rank()
 

The elliptic curves in class 2366.j have rank \(0\).

Modular form 2366.2.a.j

sage: E.q_eigenform(10)
 
\( q + q^{2} - 2q^{3} + q^{4} - 2q^{6} - q^{7} + q^{8} + q^{9} - 2q^{12} - q^{14} + q^{16} + 6q^{17} + q^{18} - 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.