Properties

Label 2.9.ag_u
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:  $1 - 6 x + 20 x^{2} - 54 x^{3} + 81 x^{4}$
Frobenius angles:  $\pm0.109926884584$, $\pm0.481195587521$
Angle rank:  $2$ (numerical)
Number field:  4.0.116032.1
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
$A(\F_{q^r})$ 42 6804 519498 41830992 3482994522 283530579444 22900885250586 1853042000237568 150102145820235546 12158399389383189684

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 86 712 6374 58984 533510 4788004 43047230 387439876 3486994886

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.