Properties

Label 2.8.ac_l
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:  $1 - 2 x + 11 x^{2} - 16 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.291254019065$, $\pm0.58248242606$
Angle rank:  $2$ (numerical)
Number field:  4.0.346176.4
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
$A(\F_{q^r})$ 58 5452 266974 16966624 1086866698 68535963436 4386134375086 281471202172800 18017806710586426 1152929253499320652

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 83 523 4143 33167 261443 2091467 16776991 134243119 1073749043

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.