Properties

Label 6600.a
Number of curves 4
Conductor 6600
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6600.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6600.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6600.a1 6600v4 [0, -1, 0, -17608, 905212] [2] 12288  
6600.a2 6600v3 [0, -1, 0, -2608, -30788] [2] 12288  
6600.a3 6600v2 [0, -1, 0, -1108, 14212] [2, 2] 6144  
6600.a4 6600v1 [0, -1, 0, 17, 712] [2] 3072 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6600.a have rank \(2\).

Modular form 6600.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{3} - 4q^{7} + q^{9} - q^{11} - 6q^{13} - 6q^{17} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.