Properties

Label 2.27.am_cw
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:  $( 1 - 10 x + 27 x^{2} )( 1 - 2 x + 27 x^{2} )$
Frobenius angles:  $\pm0.0877398280459$, $\pm0.438356648427$
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
$A(\F_{q^r})$ 468 533520 386721972 281527833600 205780798043028 150101964568941840 109421830658968892532 79766614522319063040000 58149728759974220666594388 42391161637534652006445123600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 16 734 19648 529742 14341216 387439406 10460624848 282430143518 7625596404016 205891148425214

Decomposition

1.27.ak $\times$ 1.27.ac

Base change

This is a primitive isogeny class.