Properties

Label 2.27.aq_en
Base Field $\F_{3^3}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 9 x + 27 x^{2} )( 1 - 7 x + 27 x^{2} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.264757707515$
Angle rank:  $1$ (numerical)

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

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
$A(\F_{q^r})$ 399 516705 391869072 283580621625 206042481810879 150105698825806080 109418925688395957543 79766313394870371467625 58149721846783778402490768 42391157963212715613647009025

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 708 19908 533604 14359452 387449046 10460347140 282429077316 7625595497436 205891130579268

Decomposition

1.27.aj $\times$ 1.27.ah

Base change

This is a primitive isogeny class.