# Properties

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

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 5586.u

sage: E.isogeny_class().curves

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

## Rank

sage: E.rank()

The elliptic curves in class 5586.u have rank $$1$$.

## Complex multiplication

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

## Modular form5586.2.a.u

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} - q^{12} + 4q^{13} + q^{16} - 6q^{17} + q^{18} - q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.