# Properties

 Label 188760.cq Number of curves $4$ Conductor $188760$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cq1")

sage: E.isogeny_class()

## Elliptic curves in class 188760.cq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.cq1 188760i4 $$[0, 1, 0, -6645360, -6595864992]$$ $$8945265872486162/804375$$ $$2918398728960000$$ $$[2]$$ $$4423680$$ $$2.4056$$
188760.cq2 188760i3 $$[0, 1, 0, -730880, 73252320]$$ $$11900808771122/6243874065$$ $$22653754946489272320$$ $$[2]$$ $$4423680$$ $$2.4056$$
188760.cq3 188760i2 $$[0, 1, 0, -416280, -102672000]$$ $$4397697224644/41409225$$ $$75119583283430400$$ $$[2, 2]$$ $$2211840$$ $$2.0590$$
188760.cq4 188760i1 $$[0, 1, 0, -7300, -3862432]$$ $$-94875856/14137695$$ $$-6411722007525120$$ $$[4]$$ $$1105920$$ $$1.7125$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 188760.cq have rank $$0$$.

## Complex multiplication

The elliptic curves in class 188760.cq do not have complex multiplication.

## Modular form 188760.2.a.cq

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} + q^{13} + q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.