Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("966.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 966f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
966.f4 966f1 [1, 0, 1, 4644, 858394] [6] 4800 \(\Gamma_0(N)\)-optimal
966.f2 966f2 [1, 0, 1, -111996, 13735450] [6] 9600  
966.f3 966f3 [1, 0, 1, -41931, -23576714] [2] 14400  
966.f1 966f4 [1, 0, 1, -1516491, -715440266] [2] 28800  

Rank

sage: E.rank()
 

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

Modular form 966.2.a.f

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.