Properties

Label 15246.bo
Number of curves $6$
Conductor $15246$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("15246.bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15246.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15246.bo1 15246bs4 [1, -1, 1, -1463639, 681917811] [2] 163840  
15246.bo2 15246bs5 [1, -1, 1, -995369, -378310809] [2] 327680  
15246.bo3 15246bs3 [1, -1, 1, -113279, 5221923] [2, 2] 163840  
15246.bo4 15246bs2 [1, -1, 1, -91499, 10666923] [2, 2] 81920  
15246.bo5 15246bs1 [1, -1, 1, -4379, 247371] [2] 40960 \(\Gamma_0(N)\)-optimal
15246.bo6 15246bs6 [1, -1, 1, 420331, 40013295] [2] 327680  

Rank

sage: E.rank()
 

The elliptic curves in class 15246.bo have rank \(1\).

Modular form 15246.2.a.bo

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

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.