Properties

Label 3.11.ap_dz_aqk
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:  $( 1 - 6 x + 11 x^{2} )( 1 - 9 x + 38 x^{2} - 99 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.0468428922585$, $\pm0.140218899004$, $\pm0.380176225592$
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
$A(\F_{q^r})$ 312 1505088 2325611808 3102311467008 4154340757959912 5556647549495577600 7403498659859443910808 9851799344685116613230592 13110361394916624828365551968 17449270344778098774861829700928

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 103 1314 14471 160167 1770520 19495725 214403855 2358013734 25937228503

Decomposition

1.11.ag $\times$ 2.11.aj_bm

Base change

This is a primitive isogeny class.