Properties

Label 2.27.ap_ef
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:  $1 - 15 x + 109 x^{2} - 405 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.188756140392$, $\pm0.289517143$
Angle rank:  $2$ (numerical)
Number field:  4.0.56725.1
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
$A(\F_{q^r})$ 419 527521 393675221 283669670061 206016005554064 150098244707795521 109417996076603433281 79766269688598232756725 58149726100084598712733919 42391158322494252987126167296

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 723 19999 533771 14357608 387429807 10460258269 282428922563 7625596055203 205891132324278

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.