Properties

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

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Invariants

Base field:  $\F_{2^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 4 x + 8 x^{2} )( 1 + 8 x^{2} )$
Frobenius angles:  $\pm0.25$, $\pm0.5$
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
$A(\F_{q^r})$ 45 5265 279585 16769025 1082196225 68988437505 4393755736065 281200199450625 18012199754645505 1152991875498573825

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 81 545 4097 33025 263169 2095105 16760833 134201345 1073807361

Decomposition

1.8.ae $\times$ 1.8.a

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.c_e