Properties

Label 11760ce
Number of curves 4
Conductor 11760
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("11760.br1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11760ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.br3 11760ce1 [0, 1, 0, -1976, 31380] [2] 12288 \(\Gamma_0(N)\)-optimal
11760.br2 11760ce2 [0, 1, 0, -5896, -136396] [2, 2] 24576  
11760.br1 11760ce3 [0, 1, 0, -88216, -10113580] [2] 49152  
11760.br4 11760ce4 [0, 1, 0, 13704, -834156] [2] 49152  

Rank

sage: E.rank()
 

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

Modular form 11760.2.a.br

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} + q^{9} + 6q^{13} - q^{15} - 2q^{17} - 8q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.