Properties

Label 5.2.ag_s_abi_bw_acm
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:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - 2 x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.111901318694$, $\pm0.25$, $\pm0.25$, $\pm0.359194778829$, $\pm0.729359314356$
Angle rank:  $3$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 3 2025 65403 4505625 39491733 927087525 36600767913 955088870625 36862172735193 1220220502700625

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 5 15 41 37 53 137 225 537 1105

Decomposition

1.2.ac 2 $\times$ 3.2.ac_c_ac

Base change

This is a primitive isogeny class.