Properties

Label 4.3.ah_ba_acp_fc
Base Field $\F_{3}$
Dimension $4$
$p$-rank $3$
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $4$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - 4 x + 11 x^{2} - 22 x^{3} + 33 x^{4} - 36 x^{5} + 27 x^{6} )$
Frobenius angles:  $\pm0.132091637252$, $\pm0.166666666667$, $\pm0.376445424065$, $\pm0.544359499442$
Angle rank:  $3$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 10 9380 616840 41459600 3983713550 321699331520 24298968752110 1948662891884800 154713550731961480 12105231000843656900

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 13 30 77 277 826 2321 6893 20280 58793

Decomposition

1.3.ad $\times$ 3.3.ae_l_aw

Base change

This is a primitive isogeny class.