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Properties

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

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 5610.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.c1 5610a4 \([1, 1, 0, -11968, 498988]\) \(189602977175292169/1402500\) \(1402500\) \([2]\) \(8192\) \(0.77449\)  
5610.c2 5610a3 \([1, 1, 0, -1048, 532]\) \(127483771761289/73369857660\) \(73369857660\) \([2]\) \(8192\) \(0.77449\)  
5610.c3 5610a2 \([1, 1, 0, -748, 7552]\) \(46380496070089/125888400\) \(125888400\) \([2, 2]\) \(4096\) \(0.42792\)  
5610.c4 5610a1 \([1, 1, 0, -28, 208]\) \(-2565726409/19388160\) \(-19388160\) \([2]\) \(2048\) \(0.081343\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 5610.c do not have complex multiplication.

Modular form 5610.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - q^{11} - q^{12} - 6 q^{13} + q^{15} + q^{16} - q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.