Properties

Label 2.27.am_df
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:  $1 - 12 x + 83 x^{2} - 324 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.18723158142$, $\pm0.395388412959$
Angle rank:  $2$ (numerical)
Number field:  4.0.2522128.1
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
$A(\F_{q^r})$ 477 548073 393141492 282779908569 205889210639037 150102800785953936 109421783213935793301 79766706736148639556393 58149706175390946054767508 42391146988895942760972388713

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 16 752 19972 532100 14348776 387441566 10460620312 282430470020 7625593442332 205891077277712

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.