Properties

Label 2.9.af_u
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:  $1 - 5 x + 20 x^{2} - 45 x^{3} + 81 x^{4}$
Frobenius angles:  $\pm0.225072118738$, $\pm0.476718903118$
Angle rank:  $2$ (numerical)
Number field:  4.0.39304.1
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
$A(\F_{q^r})$ 52 7904 562432 43029376 3503063252 283483725824 22882132829972 1852091916480000 150070105551338752 12157681410745985504

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 97 770 6561 59325 533422 4784085 43025153 387357170 3486788977

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.