Properties

Label 6600.y
Number of curves 4
Conductor 6600
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6600.y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6600.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6600.y1 6600bb3 [0, 1, 0, -11808, 489888] [2] 8192  
6600.y2 6600bb2 [0, 1, 0, -808, 5888] [2, 2] 4096  
6600.y3 6600bb1 [0, 1, 0, -308, -2112] [2] 2048 \(\Gamma_0(N)\)-optimal
6600.y4 6600bb4 [0, 1, 0, 2192, 41888] [2] 8192  

Rank

sage: E.rank()
 

The elliptic curves in class 6600.y have rank \(0\).

Modular form 6600.2.a.y

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{9} + q^{11} - 2q^{13} - 6q^{17} + O(q^{20}) \)

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.