Properties

Label 8400.co
Number of curves 4
Conductor 8400
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("8400.co1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8400.co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8400.co1 8400cg3 [0, 1, 0, -45008, 3659988] [2] 24576  
8400.co2 8400cg2 [0, 1, 0, -3008, 47988] [2, 2] 12288  
8400.co3 8400cg1 [0, 1, 0, -1008, -12012] [2] 6144 \(\Gamma_0(N)\)-optimal
8400.co4 8400cg4 [0, 1, 0, 6992, 307988] [4] 24576  

Rank

sage: E.rank()
 

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

Modular form 8400.2.a.co

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{7} + q^{9} + 6q^{13} - 2q^{17} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.