Properties

Label 2.27.am_cy
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:  $1 - 12 x + 76 x^{2} - 324 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.113233361917$, $\pm0.430272035486$
Angle rank:  $2$ (numerical)
Number field:  4.0.4227328.1
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
$A(\F_{q^r})$ 470 536740 388145270 281820704400 205816937709350 150106652515755940 109422828846611927270 79766784468288841420800 58149740263519243228710710 42391160248511377382673513700

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 16 738 19720 530294 14343736 387451506 10460720272 282430745246 7625597912560 205891141678818

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.