Properties

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

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

Elliptic curves in class 966.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
966.j1 966i3 \([1, 0, 0, -178849, -29127301]\) \(632678989847546725777/80515134\) \(80515134\) \([2]\) \(3840\) \(1.3770\)  
966.j2 966i4 \([1, 0, 0, -12789, -316305]\) \(231331938231569617/90942310746882\) \(90942310746882\) \([2]\) \(3840\) \(1.3770\)  
966.j3 966i2 \([1, 0, 0, -11179, -455731]\) \(154502321244119857/55101928644\) \(55101928644\) \([2, 2]\) \(1920\) \(1.0304\)  
966.j4 966i1 \([1, 0, 0, -599, -9255]\) \(-23771111713777/22848457968\) \(-22848457968\) \([4]\) \(960\) \(0.68384\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 966.j do not have complex multiplication.

Modular form 966.2.a.j

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.