Properties

Label 2.17.aj_br
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:  $1 - 9 x + 43 x^{2} - 153 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.0985547503741$, $\pm0.45562387717$
Angle rank:  $2$ (numerical)
Number field:  4.0.10525.1
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
$A(\F_{q^r})$ 171 84645 24009939 6919305525 2013747767856 582848352157005 168400935545490819 48661596480863715525 14063083404869803766211 4064238131807072897568000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 295 4887 82843 1418274 24146935 410394987 6975815443 118587867669 2015997236350

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.