Properties

Label 110466bj
Number of curves 6
Conductor 110466
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("110466.bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 110466bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
110466.bu5 110466bj1 [1, -1, 1, -110534, 13145685] [2] 884736 \(\Gamma_0(N)\)-optimal
110466.bu4 110466bj2 [1, -1, 1, -370454, -71484267] [2, 2] 1769472  
110466.bu6 110466bj3 [1, -1, 1, 734206, -417021915] [2] 3538944  
110466.bu2 110466bj4 [1, -1, 1, -5633834, -5145382587] [2, 2] 3538944  
110466.bu3 110466bj5 [1, -1, 1, -5341424, -5703534795] [2] 7077888  
110466.bu1 110466bj6 [1, -1, 1, -90140324, -329379883419] [2] 7077888  

Rank

sage: E.rank()
 

The elliptic curves in class 110466bj have rank \(0\).

Modular form 110466.2.a.bu

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + 2q^{5} + q^{8} + 2q^{10} + 4q^{11} + 2q^{13} + q^{16} - q^{17} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.