Properties

Label 2.9.af_o
Base Field $\F_{3^2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $1 - 5 x + 14 x^{2} - 45 x^{3} + 81 x^{4}$
Frobenius angles:  $\pm0.10081688066$, $\pm0.537304361732$
Angle rank:  $2$ (numerical)
Number field:  4.0.208444.1
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
$A(\F_{q^r})$ 46 6716 496984 41800384 3503142926 283272928256 22874091215966 1853149632793344 150122512267285144 12158237035604676476

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 85 680 6369 59325 533026 4782405 43049729 387492440 3486948325

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.