Properties

Label 5.2.ah_ba_acq_fg_aih
Base Field $\F_{2}$
Dimension $5$
Ordinary No
$p$-rank $5$
Contains a Jacobian No

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.0435981566527$, $\pm0.123548644961$, $\pm0.329312442367$, $\pm0.456881978294$, $\pm0.527830414776$
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 1349 31996 352089 24621781 1208552912 34419317696 1064624536593 39582728628364 1278470195863379

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 8 8 0 21 74 129 248 575 1153

Decomposition

2.2.ad_f $\times$ 3.2.ae_j_ap

Base change

This is a primitive isogeny class.