Properties

Label 5.2.ai_bg_adg_gi_ajw
Base Field $\F_{2}$
Dimension $5$
$p$-rank $0$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.0833333333333$, $\pm0.25$, $\pm0.25$, $\pm0.25$, $\pm0.583333333333$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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 1625 54925 2640625 91044641 1160290625 20848418753 848931890625 33054320493025 1128100004890625

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 5 13 33 65 65 65 193 481 1025

Decomposition

1.2.ac 3 $\times$ 2.2.ac_c

Base change

This is a primitive isogeny class.