Properties

Label 15680.bx
Number of curves $4$
Conductor $15680$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("15680.bx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15680.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15680.bx1 15680cb3 [0, 0, 0, -839468, -296028208] [2] 147456  
15680.bx2 15680cb4 [0, 0, 0, -274988, 51867088] [2] 147456  
15680.bx3 15680cb2 [0, 0, 0, -55468, -4066608] [2, 2] 73728  
15680.bx4 15680cb1 [0, 0, 0, 7252, -378672] [2] 36864 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 15680.bx have rank \(1\).

Modular form 15680.2.a.bx

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.