Properties

Label 5.2.ag_s_abo_cy_aeq
Base Field $\F_{2}$
Dimension $5$
$p$-rank $0$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )^{2}$
Frobenius angles:  $\pm0.0833333333333$, $\pm0.0833333333333$, $\pm0.25$, $\pm0.583333333333$, $\pm0.583333333333$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1 845 8125 714025 71546681 1160290625 23591416913 1249778664225 42435672150625 1124801470004225

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 5 -3 9 57 65 81 289 609 1025

Decomposition

1.2.ac $\times$ 2.2.ac_c 2

Base change

This is a primitive isogeny class.