Properties

Label 3.11.ao_dn_aoe
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:  $( 1 - 6 x + 11 x^{2} )( 1 - 8 x + 32 x^{2} - 88 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.0750991438595$, $\pm0.140218899004$, $\pm0.424900856141$
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
$A(\F_{q^r})$ 348 1566000 2313872532 3088152000000 4162394387139708 5567264082211950000 7407212135589790254708 9851819147328356352000000 13110185198708392499889484572 17449467812891781988407357150000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 108 1306 14404 160478 1773900 19505498 214404284 2357982046 25937522028

Decomposition

1.11.ag $\times$ 2.11.ai_bg

Base change

This is a primitive isogeny class.