Properties

Label 3.2.ac_ac_i
Base Field $\F_{2}$
Dimension $3$
$p$-rank $0$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - 2 x^{2} )^{2}$
Frobenius angles:  $0.0$, $0.0$, $\pm0.25$, $1.0$, $1.0$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1 5 637 2025 39401 156065 1822577 11390625 125599201 946609025

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 -3 13 9 41 33 113 161 481 897

Decomposition

1.2.ac $\times$ 2.2.a_ae

Base change

This is a primitive isogeny class.