Properties

Label 2.9.aj_bl
Base Field $\F_{3^2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $1 - 9 x + 37 x^{2} - 81 x^{3} + 81 x^{4}$
Frobenius angles:  $\pm0.114191348093$, $\pm0.309392441858$
Angle rank:  $2$ (numerical)
Number field:  4.0.2725.1
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
$A(\F_{q^r})$ 29 6061 551261 43693749 3489020624 282157981501 22875540259349 1853520335773029 150121719129767141 12158430994612350976

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 75 757 6659 59086 530931 4782709 43058339 387490393 3487003950

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.