Properties

Label 2.27.an_dq
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:  $( 1 - 8 x + 27 x^{2} )( 1 - 5 x + 27 x^{2} )$
Frobenius angles:  $\pm0.220355751984$, $\pm0.340228233311$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 460 546480 395686480 283481035200 205930114591300 150087598151420160 109417926706842456820 79766415091244043360000 58149736263891514919241040 42391155319677833250289316400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 15 749 20100 533417 14351625 387402326 10460251635 282429437393 7625597388060 205891117739789

Decomposition

1.27.ai $\times$ 1.27.af

Base change

This is a primitive isogeny class.