Properties

Label 141610.cg
Number of curves $4$
Conductor $141610$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("141610.cg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141610.cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141610.cg1 141610s3 [1, -1, 1, -3790723, 2841546481] [2] 3932160  
141610.cg2 141610s4 [1, -1, 1, -1241743, -497390743] [2] 3932160  
141610.cg3 141610s2 [1, -1, 1, -250473, 39084581] [2, 2] 1966080  
141610.cg4 141610s1 [1, -1, 1, 32747, 3625437] [2] 983040 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 141610.cg have rank \(1\).

Modular form 141610.2.a.cg

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.