Properties

Label 5.2.ag_s_abh_bs_ace
Base Field $\F_{2}$
Dimension $5$
$p$-rank $3$
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.16133478918$, $\pm0.25$, $\pm0.25$, $\pm0.327009058845$, $\pm0.739882802642$
Angle rank:  $3$ (numerical)

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1, 1]$

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
$A(\F_{q^r})$ 4 2600 100048 6890000 53126324 1040499200 32604824284 849412980000 35849268493168 1174955063165000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 5 18 49 47 62 123 193 522 1065

Decomposition

1.2.ac 2 $\times$ 3.2.ac_c_ab

Base change

This is a primitive isogeny class.