Properties

Label 2.27.ar_eu
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:  $( 1 - 10 x + 27 x^{2} )( 1 - 7 x + 27 x^{2} )$
Frobenius angles:  $\pm0.0877398280459$, $\pm0.264757707515$
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
$A(\F_{q^r})$ 378 502740 388086552 282841524000 205927500801078 150091713336358080 109417823845469404902 79766341207586283600000 58149755096744081827655928 42391166393265255495873335700

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 689 19718 532217 14351441 387412946 10460241803 282429175793 7625599857746 205891171523489

Decomposition

1.27.ak $\times$ 1.27.ah

Base change

This is a primitive isogeny class.