Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.0992589862044$, $\pm0.123548644961$, $\pm0.18645529951$, $\pm0.456881978294$, $\pm0.757883870938$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $5$
Slopes:  $[0, 0, 0, 0, 0, 1, 1, 1, 1, 1]$

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
$A(\F_{q^r})$ 1 551 22876 1393479 33501421 2168004272 63138363688 1149554681487 39154418373364 1183443090553781

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 1 3 21 32 109 207 269 570 1076

Decomposition

2.2.ad_f $\times$ 3.2.ad_c_b

Base change

This is a primitive isogeny class.