Properties

Label 6336ce
Number of curves 4
Conductor 6336
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6336.bf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6336ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6336.bf3 6336ce1 [0, 0, 0, -3180, 65104] [2] 6144 \(\Gamma_0(N)\)-optimal
6336.bf4 6336ce2 [0, 0, 0, 2580, 274768] [2] 12288  
6336.bf1 6336ce3 [0, 0, 0, -46380, -3829808] [2] 18432  
6336.bf2 6336ce4 [0, 0, 0, -23340, -7636016] [2] 36864  

Rank

sage: E.rank()
 

The elliptic curves in class 6336ce have rank \(0\).

Modular form 6336.2.a.bf

sage: E.q_eigenform(10)
 
\( q - 2q^{7} + q^{11} + 4q^{13} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.