Properties

Label 3.11.ap_ea_aqq
Base Field $\F_{11}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{11}$
Dimension:  $3$
Weil polynomial:  $( 1 - 6 x + 11 x^{2} )( 1 - 9 x + 39 x^{2} - 99 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.100899808413$, $\pm0.140218899004$, $\pm0.366706655625$
Angle rank:  $3$ (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
$A(\F_{q^r})$ 318 1539756 2374722558 3138798765024 4171825565612448 5563216585745102700 7406323568281759240038 9853404054619142247744384 13111195936794203960314102422 17449575838115732438710086890496

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 105 1341 14641 160842 1772613 19503159 214438769 2358163827 25937682600

Decomposition

1.11.ag $\times$ 2.11.aj_bn

Base change

This is a primitive isogeny class.