Properties

Label 11560a
Number of curves 4
Conductor 11560
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("11560.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11560a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11560.g3 11560a1 [0, 0, 0, -578, 4913] [2] 5120 \(\Gamma_0(N)\)-optimal
11560.g2 11560a2 [0, 0, 0, -2023, -29478] [2, 2] 10240  
11560.g1 11560a3 [0, 0, 0, -30923, -2092938] [2] 20480  
11560.g4 11560a4 [0, 0, 0, 3757, -167042] [2] 20480  

Rank

sage: E.rank()
 

The elliptic curves in class 11560a have rank \(1\).

Modular form 11560.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{5} + 4q^{7} - 3q^{9} - 4q^{11} - 2q^{13} + 4q^{19} + O(q^{20}) \)

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 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.