Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 966.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
966.f1 966f4 \([1, 0, 1, -1516491, -715440266]\) \(385693937170561837203625/2159357734550274048\) \(2159357734550274048\) \([2]\) \(28800\) \(2.3604\)  
966.f2 966f2 \([1, 0, 1, -111996, 13735450]\) \(155355156733986861625/8291568305839392\) \(8291568305839392\) \([6]\) \(9600\) \(1.8111\)  
966.f3 966f3 \([1, 0, 1, -41931, -23576714]\) \(-8152944444844179625/235342826399858688\) \(-235342826399858688\) \([2]\) \(14400\) \(2.0138\)  
966.f4 966f1 \([1, 0, 1, 4644, 858394]\) \(11079872671250375/324440155855872\) \(-324440155855872\) \([6]\) \(4800\) \(1.4645\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 966.2.a.f

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

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.