Properties

Label 112710cv
Number of curves 4
Conductor 112710
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("112710.cl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 112710cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
112710.cl4 112710cv1 [1, 0, 0, 456614, 20175716] [2] 3317760 \(\Gamma_0(N)\)-optimal
112710.cl3 112710cv2 [1, 0, 0, -1855386, 162132516] [2, 2] 6635520  
112710.cl2 112710cv3 [1, 0, 0, -18559586, -30617026404] [2] 13271040  
112710.cl1 112710cv4 [1, 0, 0, -22143186, 40035774636] [2] 13271040  

Rank

sage: E.rank()
 

The elliptic curves in class 112710cv have rank \(0\).

Modular form 112710.2.a.cl

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} - 4q^{7} + q^{8} + q^{9} - q^{10} + 4q^{11} + q^{12} + q^{13} - 4q^{14} - q^{15} + q^{16} + q^{18} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.