Properties

Label 2.3.ac_h
Base Field $\F_{3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $2$
Weil polynomial:  $( 1 - x + 3 x^{2} )^{2}$
Frobenius angles:  $\pm0.406785250661$, $\pm0.406785250661$
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
$A(\F_{q^r})$ 9 225 1296 5625 45369 518400 5157441 44555625 382124304 3431030625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 20 44 68 182 710 2354 6788 19412 58100

Decomposition

1.3.ab 2

Base change

This is a primitive isogeny class.