Properties

Label 27600.cn
Number of curves $6$
Conductor $27600$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("27600.cn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 27600.cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
27600.cn1 27600ch4 [0, 1, 0, -44160008, -112966176012] [2] 884736  
27600.cn2 27600ch6 [0, 1, 0, -10332008, 10946135988] [2] 1769472  
27600.cn3 27600ch3 [0, 1, 0, -2832008, -1668864012] [2, 2] 884736  
27600.cn4 27600ch2 [0, 1, 0, -2760008, -1765776012] [2, 2] 442368  
27600.cn5 27600ch1 [0, 1, 0, -168008, -29136012] [2] 221184 \(\Gamma_0(N)\)-optimal
27600.cn6 27600ch5 [0, 1, 0, 3515992, -8080344012] [2] 1769472  

Rank

sage: E.rank()
 

The elliptic curves in class 27600.cn have rank \(1\).

Modular form 27600.2.a.cn

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.