Properties

Label 17661.h
Number of curves 6
Conductor 17661
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("17661.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17661.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17661.h1 17661f4 [1, 0, 1, -172088802, 868900127401] [2] 1290240  
17661.h2 17661f5 [1, 0, 1, -35716447, -66790896769] [2] 2580480  
17661.h3 17661f3 [1, 0, 1, -10961612, 13028593205] [2, 2] 1290240  
17661.h4 17661f2 [1, 0, 1, -10755567, 13575848725] [2, 2] 645120  
17661.h5 17661f1 [1, 0, 1, -659362, 220588751] [2] 322560 \(\Gamma_0(N)\)-optimal
17661.h6 17661f6 [1, 0, 1, 10496503, 57824554079] [2] 2580480  

Rank

sage: E.rank()
 

The elliptic curves in class 17661.h have rank \(1\).

Modular form 17661.2.a.h

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} - q^{4} - 2q^{5} + q^{6} + q^{7} - 3q^{8} + q^{9} - 2q^{10} - 4q^{11} - q^{12} - 2q^{13} + q^{14} - 2q^{15} - q^{16} - 2q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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.