Properties

Label 5.2.ah_bc_acz_gd_aju
Base Field $\F_{2}$
Dimension $5$
$p$-rank $4$
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.123548644961$, $\pm0.25$, $\pm0.384973271919$, $\pm0.384973271919$, $\pm0.456881978294$
Angle rank:  $2$ (numerical)

Newton polygon

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1]$

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
$A(\F_{q^r})$ 4 6080 193648 1094400 19070084 1177379840 50243909132 1305229593600 33732642523216 1069747804030400

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 12 23 16 16 69 178 304 491 972

Decomposition

1.2.ac $\times$ 1.2.ab 2 $\times$ 2.2.ad_f

Base change

This is a primitive isogeny class.