Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - 4 x + 4 x^{2} + 7 x^{3} - 21 x^{4} + 14 x^{5} + 16 x^{6} - 32 x^{7} + 16 x^{8} )$
Frobenius angles:  $\pm0.0764513550391$, $\pm0.143118021706$, $\pm0.25$, $\pm0.323548644961$, $\pm0.943118021706$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 1 155 97123 1395775 55074521 918297965 34887608813 1156216740975 39849824955811 1271561917711025

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 -3 18 21 47 54 130 269 576 1147

Decomposition

1.2.ac $\times$ 4.2.ae_e_h_av

Base change

This is a primitive isogeny class.