Properties

Label 966i
Number of curves $4$
Conductor $966$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("966.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 966i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
966.j4 966i1 [1, 0, 0, -599, -9255] [4] 960 \(\Gamma_0(N)\)-optimal
966.j3 966i2 [1, 0, 0, -11179, -455731] [2, 2] 1920  
966.j1 966i3 [1, 0, 0, -178849, -29127301] [2] 3840  
966.j2 966i4 [1, 0, 0, -12789, -316305] [2] 3840  

Rank

sage: E.rank()
 

The elliptic curves in class 966i have rank \(0\).

Modular form 966.2.a.j

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.