Properties

Label 2.27.ap_eg
Base Field $\F_{3^3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 8 x + 27 x^{2} )( 1 - 7 x + 27 x^{2} )$
Frobenius angles:  $\pm0.220355751984$, $\pm0.264757707515$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 420 529200 394576560 283915800000 206051538485100 150098533296364800 109416787932994318140 79765942644422344800000 58149679790038486179484080 42391156176459917493219630000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 725 20044 534233 14360083 387430550 10460142769 282427764593 7625589982228 205891121901125

Decomposition

1.27.ai $\times$ 1.27.ah

Base change

This is a primitive isogeny class.