Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("11760.bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11760.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.bp1 11760cd7 [0, 1, 0, -275366296, -1758883007596] [2] 1327104  
11760.bp2 11760cd6 [0, 1, 0, -17210776, -27485566060] [2, 2] 663552  
11760.bp3 11760cd8 [0, 1, 0, -15956376, -31660711020] [2] 1327104  
11760.bp4 11760cd4 [0, 1, 0, -3416296, -2388827596] [2] 442368  
11760.bp5 11760cd3 [0, 1, 0, -1154456, -363230316] [2] 331776  
11760.bp6 11760cd2 [0, 1, 0, -452776, 61410740] [2, 2] 221184  
11760.bp7 11760cd1 [0, 1, 0, -390056, 93598644] [2] 110592 \(\Gamma_0(N)\)-optimal
11760.bp8 11760cd5 [0, 1, 0, 1507224, 452626740] [2] 442368  

Rank

sage: E.rank()
 

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

Modular form 11760.2.a.bp

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.