Properties

Label 11760.o
Number of curves $6$
Conductor $11760$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("11760.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11760.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.o1 11760e5 [0, -1, 0, -513536, -141471840] [2] 98304  
11760.o2 11760e3 [0, -1, 0, -33336, -2021760] [2, 2] 49152  
11760.o3 11760e2 [0, -1, 0, -8836, 291040] [2, 2] 24576  
11760.o4 11760e1 [0, -1, 0, -8591, 309366] [2] 12288 \(\Gamma_0(N)\)-optimal
11760.o5 11760e4 [0, -1, 0, 11744, 1427056] [2] 49152  
11760.o6 11760e6 [0, -1, 0, 54864, -10982880] [2] 98304  

Rank

sage: E.rank()
 

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

Modular form 11760.2.a.o

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.