Properties

Label 2.9.ae_o
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:  $1 - 4 x + 14 x^{2} - 36 x^{3} + 81 x^{4}$
Frobenius angles:  $\pm0.202305855269$, $\pm0.544090275081$
Angle rank:  $2$ (numerical)
Number field:  4.0.7168.1
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
$A(\F_{q^r})$ 56 7616 529592 43015168 3534057016 283560503744 22864993542328 1852562802327552 150096195359427128 12157330774001502656

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 94 726 6558 59846 533566 4780502 43036094 387424518 3486688414

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.