Properties

Label 11760.bx
Number of curves 8
Conductor 11760
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("11760.bx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11760.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.bx1 11760ch7 [0, 1, 0, -1505907216, -22493401078380] [2] 2359296  
11760.bx2 11760ch5 [0, 1, 0, -94119216, -351482801580] [2, 2] 1179648  
11760.bx3 11760ch8 [0, 1, 0, -93531216, -356090604780] [2] 2359296  
11760.bx4 11760ch4 [0, 1, 0, -11814896, 15622984404] [4] 589824  
11760.bx5 11760ch3 [0, 1, 0, -5919216, -5421281580] [2, 2] 589824  
11760.bx6 11760ch2 [0, 1, 0, -838896, 173166804] [2, 2] 294912  
11760.bx7 11760ch1 [0, 1, 0, 164624, 19427540] [2] 147456 \(\Gamma_0(N)\)-optimal
11760.bx8 11760ch6 [0, 1, 0, 995664, -17323173036] [2] 1179648  

Rank

sage: E.rank()
 

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

Modular form 11760.2.a.bx

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.