Properties

Label 3.11.ao_do_aok
Base Field $\F_{11}$
Dimension $3$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{11}$
Dimension:  $3$
Weil polynomial:  $( 1 - 6 x + 11 x^{2} )( 1 - 8 x + 33 x^{2} - 88 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.110710227191$, $\pm0.140218899004$, $\pm0.414323386517$
Angle rank:  $3$ (numerical)

Newton polygon

$p$-rank:  $2$
Slopes:  $[0, 0, 1/2, 1/2, 1, 1]$

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
$A(\F_{q^r})$ 354 1599372 2356790400 3115026472032 4172746362504834 5571022627031040000 7409340673826909977254 9852981256302341998891392 13110545620169884270099670400 17449477231839224547059495903052

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 110 1330 14530 160878 1775096 19511098 214429570 2358046870 25937536030

Decomposition

1.11.ag $\times$ 2.11.ai_bh

Base change

This is a primitive isogeny class.