Properties

Label 47610.bu
Number of curves 8
Conductor 47610
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("47610.bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47610.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
47610.bu1 47610bz7 [1, -1, 1, -25392893, -49244802019] [2] 2433024  
47610.bu2 47610bz8 [1, -1, 1, -2159213, -165671683] [2] 2433024  
47610.bu3 47610bz6 [1, -1, 1, -1587893, -768300019] [2, 2] 1216512  
47610.bu4 47610bz5 [1, -1, 1, -1373648, 620007581] [2] 811008  
47610.bu5 47610bz4 [1, -1, 1, -326228, -61691443] [2] 811008  
47610.bu6 47610bz2 [1, -1, 1, -88178, 9152237] [2, 2] 405504  
47610.bu7 47610bz3 [1, -1, 1, -64373, -20556403] [2] 608256  
47610.bu8 47610bz1 [1, -1, 1, 7042, 696701] [2] 202752 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 47610.bu have rank \(0\).

Modular form 47610.2.a.bu

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.