Properties

Label 2.27.am_db
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:  $1 - 12 x + 79 x^{2} - 324 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.146106651073$, $\pm0.41686804556$
Angle rank:  $2$ (numerical)
Number field:  4.0.4137232.1
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
$A(\F_{q^r})$ 473 541585 390283652 282244314825 205858236393953 150108814117538320 109423192622965966217 79766850789245174135625 58149730180634846708790308 42391153897891586287106603425

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 16 744 19828 531092 14346616 387457086 10460755048 282430980068 7625596590316 205891110834264

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.