Properties

Label 106560.ex
Number of curves $6$
Conductor $106560$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("106560.ex1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 106560.ex

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
106560.ex1 106560fo4 [0, 0, 0, -196418892, 1059553759376] [2] 10616832  
106560.ex2 106560fo6 [0, 0, 0, -174600012, -884142545776] [2] 21233664  
106560.ex3 106560fo3 [0, 0, 0, -16891212, 3000995984] [2, 2] 10616832  
106560.ex4 106560fo2 [0, 0, 0, -12283212, 16535613584] [2, 2] 5308416  
106560.ex5 106560fo1 [0, 0, 0, -486732, 449933456] [2] 2654208 \(\Gamma_0(N)\)-optimal
106560.ex6 106560fo5 [0, 0, 0, 67089588, 23929011344] [2] 21233664  

Rank

sage: E.rank()
 

The elliptic curves in class 106560.ex have rank \(0\).

Modular form 106560.2.a.ex

sage: E.q_eigenform(10)
 
\( q + q^{5} - 4q^{11} + 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.