Properties

Label 3.11.ao_dq_aoy
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:  $( 1 - 5 x + 11 x^{2} )( 1 - 9 x + 38 x^{2} - 99 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.0468428922585$, $\pm0.22822922288$, $\pm0.380176225592$
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
$A(\F_{q^r})$ 364 1658384 2428264384 3141808488000 4160796310194524 5552650547255791616 7399139569679725554596 9849401810274620569248000 13109462011571487576054074944 17449067883631065464897552341904

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 114 1372 14658 160418 1769244 19484246 214351682 2357851972 25936927554

Decomposition

1.11.af $\times$ 2.11.aj_bm

Base change

This is a primitive isogeny class.