Properties

Label 11760.b
Number of curves $6$
Conductor $11760$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("11760.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11760.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.b1 11760br5 [0, -1, 0, -13171216, -18394301120] [2] 294912  
11760.b2 11760br3 [0, -1, 0, -823216, -287193920] [2, 2] 147456  
11760.b3 11760br6 [0, -1, 0, -768336, -327190464] [2] 294912  
11760.b4 11760br4 [0, -1, 0, -290096, 56938176] [2] 147456  
11760.b5 11760br2 [0, -1, 0, -54896, -3837504] [2, 2] 73728  
11760.b6 11760br1 [0, -1, 0, 7824, -375360] [2] 36864 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11760.b have rank \(1\).

Modular form 11760.2.a.b

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.