Properties

Label 5.2.ag_q_ay_w_au
Base Field $\F_{2}$
Dimension $5$
Ordinary No
$p$-rank $0$
Contains a Jacobian No

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - 4 x + 6 x^{2} - 4 x^{3} + 2 x^{4} - 8 x^{5} + 24 x^{6} - 32 x^{7} + 16 x^{8} )$
Frobenius angles:  $\pm0.0377785699724$, $\pm0.148391828106$, $\pm0.25$, $\pm0.398391828106$, $\pm0.787778569972$
Angle rank:  $2$ (numerical)

Newton polygon

$p$-rank:  $0$
Slopes:  $[1/4, 1/4, 1/4, 1/4, 1/2, 1/2, 3/4, 3/4, 3/4, 3/4]$

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
$A(\F_{q^r})$ 1 485 34957 1690225 18761641 1237652585 36577681561 1028469798225 35261765927713 979140494205425

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 1 9 25 17 73 137 241 513 881

Decomposition

1.2.ac $\times$ 4.2.ae_g_ae_c

Base change

This is a primitive isogeny class.