Properties

Label 2.8.ad_n
Base Field $\F_{2^3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2^3}$
Dimension:  $2$
Weil polynomial:  $1 - 3 x + 13 x^{2} - 24 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.266203455796$, $\pm0.544672082212$
Angle rank:  $2$ (numerical)
Number field:  4.0.243873.1
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
$A(\F_{q^r})$ 51 5355 271728 16841475 1087514871 68817833280 4387481108187 281289296391075 18016362755695152 1152967524456442275

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 82 531 4114 33186 262519 2092110 16766146 134232363 1073784682

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.