Properties

Label 6336cc
Number of curves 4
Conductor 6336
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("6336.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6336cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6336.n3 6336cc1 [0, 0, 0, -3756, -87856] [2] 6144 \(\Gamma_0(N)\)-optimal
6336.n2 6336cc2 [0, 0, 0, -6636, 65360] [2, 2] 12288  
6336.n1 6336cc3 [0, 0, 0, -84396, 9427664] [2] 24576  
6336.n4 6336cc4 [0, 0, 0, 25044, 508880] [2] 24576  

Rank

sage: E.rank()
 

The elliptic curves in class 6336cc have rank \(1\).

Modular form 6336.2.a.n

sage: E.q_eigenform(10)
 
\( q - 2q^{5} - 4q^{7} - q^{11} + 2q^{13} + 2q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.