Properties

Label 7650by
Number of curves 4
Conductor 7650
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("7650.ci1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7650by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7650.ci4 7650by1 [1, -1, 1, -680, -4053] [2] 6912 \(\Gamma_0(N)\)-optimal
7650.ci3 7650by2 [1, -1, 1, -9680, -364053] [2] 13824  
7650.ci2 7650by3 [1, -1, 1, -23180, 1363947] [2] 20736  
7650.ci1 7650by4 [1, -1, 1, -25430, 1084947] [2] 41472  

Rank

sage: E.rank()
 

The elliptic curves in class 7650by have rank \(1\).

Modular form 7650.2.a.ci

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

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 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.