Properties

Label 5586.y
Number of curves $4$
Conductor $5586$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5586.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5586.y1 5586bb3 \([1, 0, 0, -4290049, 3419763689]\) \(74220219816682217473/16416\) \(1931325984\) \([2]\) \(92160\) \(2.0744\)  
5586.y2 5586bb2 \([1, 0, 0, -268129, 53416649]\) \(18120364883707393/269485056\) \(31704647353344\) \([2, 2]\) \(46080\) \(1.7278\)  
5586.y3 5586bb4 \([1, 0, 0, -260289, 56689065]\) \(-16576888679672833/2216253521952\) \(-260740010604130848\) \([2]\) \(92160\) \(2.0744\)  
5586.y4 5586bb1 \([1, 0, 0, -17249, 782025]\) \(4824238966273/537919488\) \(63285689843712\) \([2]\) \(23040\) \(1.3812\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5586.y have rank \(1\).

Complex multiplication

The elliptic curves in class 5586.y do not have complex multiplication.

Modular form 5586.2.a.y

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.