Properties

Label 2.9.af_t
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:  $1 - 5 x + 19 x^{2} - 45 x^{3} + 81 x^{4}$
Frobenius angles:  $\pm0.20560185004$, $\pm0.488925242199$
Angle rank:  $2$ (numerical)
Number field:  4.0.206829.1
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
$A(\F_{q^r})$ 51 7701 551259 42886869 3510481776 283765531581 22885818795051 1852229019804549 150076340564816619 12157647140529874176

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 95 755 6539 59450 533951 4784855 43028339 387373265 3486779150

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.