Properties

Label 8400.cn
Number of curves $8$
Conductor $8400$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("8400.cn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8400.cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8400.cn1 8400ce7 [0, 1, 0, -2580408, -1004608812] [2] 331776  
8400.cn2 8400ce4 [0, 1, 0, -2304408, -1347208812] [2] 110592  
8400.cn3 8400ce6 [0, 1, 0, -1080408, 420391188] [2, 2] 165888  
8400.cn4 8400ce3 [0, 1, 0, -1072408, 427095188] [2] 82944  
8400.cn5 8400ce2 [0, 1, 0, -144408, -20968812] [2, 2] 55296  
8400.cn6 8400ce5 [0, 1, 0, -32408, -52552812] [2] 110592  
8400.cn7 8400ce1 [0, 1, 0, -16408, 279188] [2] 27648 \(\Gamma_0(N)\)-optimal
8400.cn8 8400ce8 [0, 1, 0, 291592, 1416463188] [2] 331776  

Rank

sage: E.rank()
 

The elliptic curves in class 8400.cn have rank \(0\).

Modular form 8400.2.a.cn

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{7} + q^{9} - 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.