Properties

Label 52800.cv
Number of curves 4
Conductor 52800
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("52800.cv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 52800.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
52800.cv1 52800eg3 [0, -1, 0, -128833, 17773537] [2] 331776  
52800.cv2 52800eg4 [0, -1, 0, -64833, 35373537] [2] 663552  
52800.cv3 52800eg1 [0, -1, 0, -8833, -298463] [2] 110592 \(\Gamma_0(N)\)-optimal
52800.cv4 52800eg2 [0, -1, 0, 7167, -1274463] [2] 221184  

Rank

sage: E.rank()
 

The elliptic curves in class 52800.cv have rank \(0\).

Modular form 52800.2.a.cv

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

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 LMFDB 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 LMFDB labels.