Properties

Label 966g
Number of curves 6
Conductor 966
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("966.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 966g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
966.g5 966g1 [1, 1, 1, 126, 1167] [4] 512 \(\Gamma_0(N)\)-optimal
966.g4 966g2 [1, 1, 1, -1154, 12431] [2, 4] 1024  
966.g3 966g3 [1, 1, 1, -5074, -128689] [2, 2] 2048  
966.g2 966g4 [1, 1, 1, -17714, 900047] [8] 2048  
966.g1 966g5 [1, 1, 1, -79134, -8601153] [2] 4096  
966.g6 966g6 [1, 1, 1, 6266, -609505] [2] 4096  

Rank

sage: E.rank()
 

The elliptic curves in class 966g have rank \(1\).

Modular form 966.2.a.g

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - 2q^{5} - q^{6} + q^{7} + q^{8} + q^{9} - 2q^{10} - 4q^{11} - q^{12} - 2q^{13} + q^{14} + 2q^{15} + q^{16} - 6q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.