# Properties

 Label 189618bq Number of curves $6$ Conductor $189618$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bq1")

sage: E.isogeny_class()

## Elliptic curves in class 189618bq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.l5 189618bq1 $$[1, 1, 0, -47999, 3045957]$$ $$2533811507137/625016832$$ $$3016836869849088$$ $$[2]$$ $$1179648$$ $$1.6807$$ $$\Gamma_0(N)$$-optimal
189618.l4 189618bq2 $$[1, 1, 0, -264319, -49865915]$$ $$423108074414017/23284318464$$ $$112388957920901376$$ $$[2, 2]$$ $$2359296$$ $$2.0273$$
189618.l6 189618bq3 $$[1, 1, 0, 181841, -200578763]$$ $$137763859017023/3683199928848$$ $$-17778102565362886032$$ $$[2]$$ $$4718592$$ $$2.3738$$
189618.l2 189618bq4 $$[1, 1, 0, -4171599, -3281186475]$$ $$1663303207415737537/5483698704$$ $$26468766257755536$$ $$[2, 2]$$ $$4718592$$ $$2.3738$$
189618.l3 189618bq5 $$[1, 1, 0, -4114139, -3375892047]$$ $$-1595514095015181697/95635786040388$$ $$-461615672781819161892$$ $$[2]$$ $$9437184$$ $$2.7204$$
189618.l1 189618bq6 $$[1, 1, 0, -66745539, -209912851143]$$ $$6812873765474836663297/74052$$ $$357434860068$$ $$[2]$$ $$9437184$$ $$2.7204$$

## Rank

sage: E.rank()

The elliptic curves in class 189618bq have rank $$1$$.

## Complex multiplication

The elliptic curves in class 189618bq do not have complex multiplication.

## Modular form 189618.2.a.bq

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + 2q^{5} + q^{6} - q^{8} + q^{9} - 2q^{10} + q^{11} - q^{12} - 2q^{15} + q^{16} + q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.