Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} )^{3}$
Frobenius angles:  $0.0$, $0.0$, $\pm0.25$, $\pm0.25$, $\pm0.25$, $1.0$, $1.0$
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 is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1 125 107653 1265625 66233081 659374625 23272485713 576650390625 29058756742561 994531106890625

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 -3 21 25 57 33 81 97 417 897

Decomposition

1.2.ac 3 $\times$ 2.2.a_ae

Base change

This is a primitive isogeny class.