Properties

Label 2.17.ak_cb
Base Field $\F_{17}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{17}$
Dimension:  $2$
Weil polynomial:  $1 - 10 x + 53 x^{2} - 170 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.141075462221$, $\pm0.399907016694$
Angle rank:  $2$ (numerical)
Number field:  4.0.442944.2
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
$A(\F_{q^r})$ 163 85249 24536716 6970725481 2014644459643 582758684476816 168407869599292507 48663207639232067529 14063113492007835514444 4064227265971277058006049

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 296 4994 83460 1418908 24143222 410411884 6976046404 118588121378 2015991846536

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.