Properties

Label 25872bx
Number of curves 6
Conductor 25872
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("25872.bf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25872bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25872.bf4 25872bx1 [0, -1, 0, -26672, 1684992] [2] 61440 \(\Gamma_0(N)\)-optimal
25872.bf3 25872bx2 [0, -1, 0, -30592, 1161280] [2, 2] 122880  
25872.bf6 25872bx3 [0, -1, 0, 98768, 8301952] [2] 245760  
25872.bf2 25872bx4 [0, -1, 0, -222672, -39559680] [2, 2] 245760  
25872.bf5 25872bx5 [0, -1, 0, 24288, -122735808] [4] 491520  
25872.bf1 25872bx6 [0, -1, 0, -3542912, -2565598272] [2] 491520  

Rank

sage: E.rank()
 

The elliptic curves in class 25872bx have rank \(0\).

Modular form 25872.2.a.bf

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

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 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.