Properties

Label 2.17.aj_bs
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:  $1 - 9 x + 44 x^{2} - 153 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.116336544503$, $\pm0.449669877836$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}, \sqrt{41})\)
Galois group:  $V_4$

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
$A(\F_{q^r})$ 172 85312 24143296 6931770624 2014449490252 582898741743616 168406571598364684 48661978739878425600 14063084451840828627904 4064236334561133871365952

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 297 4914 82993 1418769 24149022 410408721 6975870241 118587876498 2015996344857

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.