Properties

Label 2.17.ai_bg
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:  $1 - 8 x + 32 x^{2} - 136 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.00936746300954$, $\pm0.50936746301$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\zeta_{8})\)
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
$A(\F_{q^r})$ 178 82948 23402194 6880370704 2013144841618 582622191933700 168358154431328242 48658925715634520064 14063027005371573629746 4064231406644218986637828

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 290 4762 82374 1417850 24137570 410290730 6975432574 118587392074 2015993900450

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.