Properties

Label 7650bz
Number of curves 6
Conductor 7650
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("7650.ca1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7650bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7650.ca5 7650bz1 [1, -1, 1, -7655, -237153] [2] 16384 \(\Gamma_0(N)\)-optimal
7650.ca4 7650bz2 [1, -1, 1, -25655, 1310847] [2, 2] 32768  
7650.ca2 7650bz3 [1, -1, 1, -390155, 93893847] [2, 2] 65536  
7650.ca6 7650bz4 [1, -1, 1, 50845, 7583847] [2] 65536  
7650.ca1 7650bz5 [1, -1, 1, -6242405, 6004666347] [2] 131072  
7650.ca3 7650bz6 [1, -1, 1, -369905, 104059347] [2] 131072  

Rank

sage: E.rank()
 

The elliptic curves in class 7650bz have rank \(0\).

Modular form 7650.2.a.ca

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.