Properties

Label 3.11.aq_eo_ati
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:  $( 1 - 6 x + 11 x^{2} )( 1 - 5 x + 11 x^{2} )^{2}$
Frobenius angles:  $\pm0.140218899004$, $\pm0.22822922288$, $\pm0.22822922288$
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
$A(\F_{q^r})$ 294 1529388 2473452576 3249949500000 4227425799974454 5573941210112486400 7401573355048140841314 9848682797040213462000000 13109296997460963836814159456 17449193974096987274709084680748

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 102 1394 15154 162976 1776024 19490656 214336034 2357822294 25937114982

Decomposition

1.11.ag $\times$ 1.11.af 2

Base change

This is a primitive isogeny class.