Properties

Label 2.27.ao_dr
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:  $1 - 14 x + 95 x^{2} - 378 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.105338029469$, $\pm0.368520329433$
Angle rank:  $2$ (numerical)
Number field:  4.0.66112.2
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
$A(\F_{q^r})$ 433 526961 389623792 282304073881 205804575250433 150088763834792192 109420970706011081753 79767003572825684409513 58149801494518770720139504 42391160853828414638317902641

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 14 724 19796 531204 14342874 387405334 10460542638 282431521028 7625605942220 205891144618804

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.