Properties

Label 2.27.am_di
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:  $( 1 - 8 x + 27 x^{2} )( 1 - 4 x + 27 x^{2} )$
Frobenius angles:  $\pm0.220355751984$, $\pm0.374235869875$
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
$A(\F_{q^r})$ 480 552960 395290080 283159756800 205894382258400 150091782518108160 109419489866575930080 79766522553408395673600 58149711899972659632745440 42391149457613914052465356800

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 16 758 20080 532814 14349136 387413126 10460401072 282429817886 7625594193040 205891089268118

Decomposition

1.27.ai $\times$ 1.27.ae

Base change

This is a primitive isogeny class.