Properties

Label 2.19.aj_bp
Base Field $\F_{19}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{19}$
Dimension:  $2$
Weil polynomial:  $1 - 9 x + 41 x^{2} - 171 x^{3} + 361 x^{4}$
Frobenius angles:  $\pm0.0387402455333$, $\pm0.487338161656$
Angle rank:  $2$ (numerical)
Number field:  4.0.404685.1
Galois group:  $D_4$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 223 130009 46130449 16808213565 6123139391248 2213461142579401 798986180611862053 288434720228854856085 104127054027894241747699 37589990931555184078299904

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 363 6725 128971 2472896 47048991 893848799 16983168931 322686779645 6131069107878

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.