Properties

Label 11760.bg
Number of curves $4$
Conductor $11760$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11760.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.bg1 11760bx3 [0, -1, 0, -292840, 61092592] [2] 73728  
11760.bg2 11760bx2 [0, -1, 0, -18440, 944112] [2, 2] 36864  
11760.bg3 11760bx1 [0, -1, 0, -2760, -34320] [2] 18432 \(\Gamma_0(N)\)-optimal
11760.bg4 11760bx4 [0, -1, 0, 5080, 3164400] [2] 73728  

Rank

sage: E.rank()
 

The elliptic curves in class 11760.bg have rank \(0\).

Complex multiplication

The elliptic curves in class 11760.bg do not have complex multiplication.

Modular form 11760.2.a.bg

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.