Properties

Label 2.27.am_de
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:  $1 - 12 x + 82 x^{2} - 324 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.17689420165$, $\pm0.401281784543$
Angle rank:  $2$ (numerical)
Number field:  4.0.47104.1
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
$A(\F_{q^r})$ 476 546448 392426300 282649135104 205884047483996 150105243209933200 109422322724933782844 79766759198793102557184 58149710536165048234286300 42391147952268238900111274128

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 16 750 19936 531854 14348416 387447870 10460671888 282430655774 7625594014192 205891081956750

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.