Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5586.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5586.t1 5586w4 \([1, 1, 1, -59634, 5580315]\) \(199350693197713/547428\) \(64404356772\) \([2]\) \(12288\) \(1.3072\)  
5586.t2 5586w3 \([1, 1, 1, -10634, -316933]\) \(1130389181713/295568028\) \(34773282926172\) \([2]\) \(12288\) \(1.3072\)  
5586.t3 5586w2 \([1, 1, 1, -3774, 83691]\) \(50529889873/2547216\) \(299677415184\) \([2, 2]\) \(6144\) \(0.96064\)  
5586.t4 5586w1 \([1, 1, 1, 146, 5291]\) \(2924207/102144\) \(-12017139456\) \([4]\) \(3072\) \(0.61407\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5586.2.a.t

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.