Properties

Label 5.2.ag_q_au_e_q
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:  $( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x^{2} + 4 x^{4} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.25$, $\pm0.25$, $\pm0.25$, $\pm0.833333333333$
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
$A(\F_{q^r})$ 3 1125 177957 6890625 68438553 1801814625 23457176529 848931890625 29286667687329 1061866923890625

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 1 21 49 57 97 81 193 417 961

Decomposition

1.2.ac 3 $\times$ 2.2.a_ac

Base change

This is a primitive isogeny class.