Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5586u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5586.u3 5586u1 \([1, 1, 1, -393, -393]\) \(57066625/32832\) \(3862651968\) \([2]\) \(3456\) \(0.52915\) \(\Gamma_0(N)\)-optimal
5586.u4 5586u2 \([1, 1, 1, 1567, -1177]\) \(3616805375/2105352\) \(-247692557448\) \([2]\) \(6912\) \(0.87572\)  
5586.u1 5586u3 \([1, 1, 1, -20973, 1160319]\) \(8671983378625/82308\) \(9683453892\) \([2]\) \(10368\) \(1.0785\)  
5586.u2 5586u4 \([1, 1, 1, -20483, 1217747]\) \(-8078253774625/846825858\) \(-99628215367842\) \([2]\) \(20736\) \(1.4250\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5586.2.a.u

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.