Properties

Label 3.4.ag_u_abt
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:  $( 1 - 3 x + 4 x^{2} )( 1 - 3 x + 7 x^{2} - 12 x^{3} + 16 x^{4} )$
Frobenius angles:  $\pm0.190783854037$, $\pm0.230053456163$, $\pm0.524117187371$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 18 5616 311688 18296928 1234885518 73518471936 4374427025322 277585512414912 17945844611747832 1151079557883059376

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 21 74 281 1169 4374 16295 64625 261146 1046901

Decomposition

1.4.ad $\times$ 2.4.ad_h

Base change

This is a primitive isogeny class.