Properties

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

Learn more about

Invariants

Base field:  $\F_{3^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 9 x + 27 x^{2} )( 1 - 4 x + 27 x^{2} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.374235869875$
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
$A(\F_{q^r})$ 456 539904 392577696 282825470976 205885332491736 150098947725275136 109421627674767211896 79766893306551827288064 58149753956741175359781024 42391151244366428978991469824

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 15 741 19944 532185 14348505 387431622 10460605443 282431130609 7625599708248 205891097946261

Decomposition

1.27.aj $\times$ 1.27.ae

Base change

This is a primitive isogeny class.