Properties

Label 2.27.an_dk
Base Field $\F_{3^3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{3^3}$
Dimension:  $2$
Weil polynomial:  $1 - 13 x + 88 x^{2} - 351 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.142210682091$, $\pm0.386495029441$
Angle rank:  $2$ (numerical)
Number field:  4.0.2082168.1
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
$A(\F_{q^r})$ 454 536628 391026568 282485272224 205851767201674 150100080906776256 109422415853326865722 79767003368630884902528 58149766707397287149591464 42391154321959896864456950388

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 15 737 19866 531545 14346165 387434546 10460680791 282431520305 7625601380334 205891112893937

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.