Properties

Label 11154bf
Number of curves 4
Conductor 11154
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("11154.bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11154bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11154.bg3 11154bf1 [1, 0, 0, -933, 10269] [2] 8640 \(\Gamma_0(N)\)-optimal
11154.bg4 11154bf2 [1, 0, 0, 757, 43731] [2] 17280  
11154.bg1 11154bf3 [1, 0, 0, -13608, -609792] [2] 25920  
11154.bg2 11154bf4 [1, 0, 0, -6848, -1214136] [2] 51840  

Rank

sage: E.rank()
 

The elliptic curves in class 11154bf have rank \(0\).

Modular form 11154.2.a.bg

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{6} - 2q^{7} + q^{8} + q^{9} + q^{11} + q^{12} - 2q^{14} + q^{16} - 6q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.