Properties

Label 2.17.aj_bx
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:  $1 - 9 x + 49 x^{2} - 153 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.191982029838$, $\pm0.413688260814$
Angle rank:  $2$ (numerical)
Number field:  4.0.609021.1
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
$A(\F_{q^r})$ 177 88677 24814161 6989255109 2016042350352 582819653602341 168401400838004049 48661717364683726725 14062978166342579447409 4064220658854933316042752

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 307 5049 83683 1419894 24145747 410396121 6975832771 118586980233 2015988569182

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.