Properties

Label 3.4.ag_s_abn
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 4 x^{2} )( 1 - 3 x + 5 x^{2} - 12 x^{3} + 16 x^{4} )$
Frobenius angles:  $\pm0.103279877171$, $\pm0.230053456163$, $\pm0.563386789496$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

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
$A(\F_{q^r})$ 14 4144 232064 16783200 1200183614 71163817984 4351584693806 281474974468800 18082993331747456 1152921506652542704

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 17 56 257 1139 4238 16211 65537 263144 1048577

Decomposition

1.4.ad $\times$ 2.4.ad_f

Base change

This is a primitive isogeny class.