Properties

Label 116610.bb
Number of curves $6$
Conductor $116610$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("116610.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116610.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
116610.bb1 116610y4 [1, 0, 1, -18657604, 31017738806] [2] 3538944  
116610.bb2 116610y6 [1, 0, 1, -4365274, -3007392178] [2] 7077888  
116610.bb3 116610y3 [1, 0, 1, -1196524, 457952822] [2, 2] 3538944  
116610.bb4 116610y2 [1, 0, 1, -1166104, 484576406] [2, 2] 1769472  
116610.bb5 116610y1 [1, 0, 1, -70984, 7980182] [2] 884736 \(\Gamma_0(N)\)-optimal
116610.bb6 116610y5 [1, 0, 1, 1485506, 2219510126] [2] 7077888  

Rank

sage: E.rank()
 

The elliptic curves in class 116610.bb have rank \(2\).

Modular form 116610.2.a.bb

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} - 4q^{11} + q^{12} - q^{15} + q^{16} - 6q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.