Properties

Label 2.8.ai_bg
Base Field $\F_{2^3}$
Dimension $2$
$p$-rank $0$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{2^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 4 x + 8 x^{2} )^{2}$
Frobenius angles:  $\pm0.25$, $\pm0.25$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

$p$-rank:  $0$
Slopes:  $[1/2, 1/2, 1/2, 1/2]$

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
$A(\F_{q^r})$ 25 4225 297025 17850625 1090650625 68720001025 4389464961025 281200199450625 18010000999809025 1152921506754330625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 65 577 4353 33281 262145 2093057 16760833 134184961 1073741825

Decomposition

1.8.ae 2

Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{2^3}$.

SubfieldPrimitive Model
$\F_{2}$2.2.e_i
$\F_{2}$2.2.ac_c