Properties

Label 5.2.ah_y_acc_dp_afi
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:  $( 1 - 2 x + 2 x^{2} )( 1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8} )$
Frobenius angles:  $\pm0.0635622003031$, $\pm0.165221137389$, $\pm0.25$, $\pm0.365221137389$, $\pm0.663562200303$
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
$A(\F_{q^r})$ 1 1055 24193 2220775 42917611 791232065 38912485753 1259679099375 32800858440571 1123122764602025

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 4 8 28 41 46 143 292 476 1019

Decomposition

1.2.ac $\times$ 4.2.af_m_au_bd

Base change

This is a primitive isogeny class.