Properties

Label 6600bb
Number of curves $4$
Conductor $6600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 6600bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6600.y3 6600bb1 \([0, 1, 0, -308, -2112]\) \(810448/33\) \(132000000\) \([2]\) \(2048\) \(0.32398\) \(\Gamma_0(N)\)-optimal
6600.y2 6600bb2 \([0, 1, 0, -808, 5888]\) \(3650692/1089\) \(17424000000\) \([2, 2]\) \(4096\) \(0.67056\)  
6600.y1 6600bb3 \([0, 1, 0, -11808, 489888]\) \(5690357426/891\) \(28512000000\) \([2]\) \(8192\) \(1.0171\)  
6600.y4 6600bb4 \([0, 1, 0, 2192, 41888]\) \(36382894/43923\) \(-1405536000000\) \([2]\) \(8192\) \(1.0171\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 6600bb do not have complex multiplication.

Modular form 6600.2.a.bb

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.