Properties

Label 5.2.ag_s_abk_cf_ade
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:  $( 1 - 2 x + 2 x^{2} )( 1 - 4 x + 8 x^{2} - 12 x^{3} + 17 x^{4} - 24 x^{5} + 32 x^{6} - 32 x^{7} + 16 x^{8} )$
Frobenius angles:  $\pm0.0755571399449$, $\pm0.203216343788$, $\pm0.25$, $\pm0.424442860055$, $\pm0.703216343788$
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
$A(\F_{q^r})$ 2 1460 31226 2131600 38133362 1116954020 45547817842 962596454400 28494805076114 1124768298875300

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 5 9 29 37 65 165 221 405 1025

Decomposition

1.2.ac $\times$ 4.2.ae_i_am_r

Base change

This is a primitive isogeny class.