Properties

Label 266805.bq
Number of curves $6$
Conductor $266805$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("266805.bq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 266805.bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
266805.bq1 266805bq5 [1, -1, 1, -707034362, 7236002234486] [2] 94371840  
266805.bq2 266805bq3 [1, -1, 1, -46691987, 99550119386] [2, 2] 47185920  
266805.bq3 266805bq2 [1, -1, 1, -14408582, -19653125236] [2, 2] 23592960  
266805.bq4 266805bq1 [1, -1, 1, -14141777, -20465706544] [2] 11796480 \(\Gamma_0(N)\)-optimal
266805.bq5 266805bq4 [1, -1, 1, 13605943, -86854367806] [2] 47185920  
266805.bq6 266805bq6 [1, -1, 1, 97115908, 591718259234] [2] 94371840  

Rank

sage: E.rank()
 

The elliptic curves in class 266805.bq have rank \(1\).

Modular form 266805.2.a.bq

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{4} + q^{5} + 3q^{8} - q^{10} - 2q^{13} - q^{16} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.