Properties

Label 2.17.al_cj
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:  $1 - 11 x + 61 x^{2} - 187 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.153753248596$, $\pm0.352010293509$
Angle rank:  $2$ (numerical)
Number field:  4.0.134693.2
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
$A(\F_{q^r})$ 153 83997 24739641 7006777749 2016056118528 582629752607373 168392104113976497 48663041996611347237 14063184164576808156897 4064230371874251183132672

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 291 5035 83891 1419902 24137883 410373467 6976022659 118588717327 2015993387166

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.