Properties

Label 2.27.ar_ev
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:  $1 - 17 x + 125 x^{2} - 459 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.123648726268$, $\pm0.248545709748$
Angle rank:  $2$ (numerical)
Number field:  4.0.20725.1
Galois group:  $D_4$

This isogeny class is simple.

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
$A(\F_{q^r})$ 379 504449 389111341 283192119661 206009238671984 150105560196656801 109419476903054268329 79766443103704721344629 58149745520712275876402119 42391162356933336999140321024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 691 19769 532875 14357136 387448687 10460399835 282429536579 7625598601973 205891151919286

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.