Properties

Label 2.17.aj_bp
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:  $1 - 9 x + 41 x^{2} - 153 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.0511302365929$, $\pm0.466745019538$
Angle rank:  $2$ (numerical)
Number field:  4.0.328653.3
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
$A(\F_{q^r})$ 169 83317 23743993 6893398629 2011960631824 582679036603573 168381752616945673 48660082030956511557 14063008289407622370553 4064234484501891974889472

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 291 4833 82531 1417014 24139923 410348241 6975598339 118587234249 2015995427166

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.