Properties

Label 5610m
Number of curves $4$
Conductor $5610$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("5610.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5610m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5610.n3 5610m1 [1, 0, 1, -139, -538] [2] 2304 \(\Gamma_0(N)\)-optimal
5610.n2 5610m2 [1, 0, 1, -639, 5662] [2, 2] 4608  
5610.n1 5610m3 [1, 0, 1, -9989, 383402] [2] 9216  
5610.n4 5610m4 [1, 0, 1, 711, 26722] [2] 9216  

Rank

sage: E.rank()
 

The elliptic curves in class 5610m have rank \(1\).

Modular form 5610.2.a.n

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} + q^{11} + q^{12} - 2q^{13} - q^{15} + q^{16} - q^{17} - q^{18} + O(q^{20}) \)

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.