Properties

Label 2.27.ao_dz
Base Field $\F_{3^3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 7 x + 27 x^{2} )^{2}$
Frobenius angles:  $\pm0.264757707515$, $\pm0.264757707515$
Angle rank:  $1$ (numerical)

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
$A(\F_{q^r})$ 441 540225 396328464 283955765625 206005480057881 150086260157702400 109415156282457620049 79765883525066979515625 58149706690516196282574096 42391163559834762025908830625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 14 740 20132 534308 14356874 387398870 10459986782 282427555268 7625593509884 205891157761700

Decomposition

1.27.ah 2

Base change

This is a primitive isogeny class.