Properties

Label 2.8.af_v
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:  $1 - 5 x + 21 x^{2} - 40 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.279106592915$, $\pm0.421442037109$
Angle rank:  $2$ (numerical)
Number field:  4.0.14225.1
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
$A(\F_{q^r})$ 41 5371 300284 16977731 1066394461 68604083776 4398032021249 281426689045475 18012040556369516 1152922252493109571

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 82 583 4146 32544 261703 2097148 16774338 134200159 1073742522

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.