Properties

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

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Invariants

Base field:  $\F_{17}$
Dimension:  $2$
Weil polynomial:  $1 - 13 x + 75 x^{2} - 221 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.125047581931$, $\pm0.273653339326$
Angle rank:  $2$ (numerical)
Number field:  4.0.9725.1
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
$A(\F_{q^r})$ 131 78469 24460451 7022112341 2018655589936 582687837815581 168377148446907251 48661391770783328069 14063150365174514584619 4064239321923284317498624

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 271 4979 84075 1421730 24140287 410337023 6975786099 118588432313 2015997826686

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.