Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 11560a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11560.g3 11560a1 \([0, 0, 0, -578, 4913]\) \(55296/5\) \(1931005520\) \([2]\) \(5120\) \(0.52125\) \(\Gamma_0(N)\)-optimal
11560.g2 11560a2 \([0, 0, 0, -2023, -29478]\) \(148176/25\) \(154480441600\) \([2, 2]\) \(10240\) \(0.86782\)  
11560.g1 11560a3 \([0, 0, 0, -30923, -2092938]\) \(132304644/5\) \(123584353280\) \([2]\) \(20480\) \(1.2144\)  
11560.g4 11560a4 \([0, 0, 0, 3757, -167042]\) \(237276/625\) \(-15448044160000\) \([2]\) \(20480\) \(1.2144\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 11560a do not have complex multiplication.

Modular form 11560.2.a.a

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

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.