Properties

Label 6336.cg
Number of curves 2
Conductor 6336
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6336.cg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6336.cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6336.cg1 6336ca2 [0, 0, 0, -444, -1712] [2] 3072  
6336.cg2 6336ca1 [0, 0, 0, 96, -200] [2] 1536 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 6336.2.a.cg

sage: E.q_eigenform(10)
 
\( q + 2q^{5} + 2q^{7} - q^{11} + 2q^{13} - 4q^{17} - 6q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.