Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("6336.cd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6336.cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6336.cd1 6336z3 [0, 0, 0, -17004, -853328] [2] 8192  
6336.cd2 6336z2 [0, 0, 0, -1164, -10640] [2, 2] 4096  
6336.cd3 6336z1 [0, 0, 0, -444, 3472] [2] 2048 \(\Gamma_0(N)\)-optimal
6336.cd4 6336z4 [0, 0, 0, 3156, -71120] [2] 8192  

Rank

sage: E.rank()
 

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

Modular form 6336.2.a.cd

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

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 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.