Properties

Label 3.11.ao_dt_apo
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:  $( 1 - 6 x + 11 x^{2} )( 1 - 4 x + 11 x^{2} )^{2}$
Frobenius angles:  $\pm0.140218899004$, $\pm0.2939628337$, $\pm0.2939628337$
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
$A(\F_{q^r})$ 384 1769472 2575440000 3238162071552 4193575548057984 5554939751424000000 7397001190199816697984 9849772122421444038623232 13110838543808696379936240000 17449893435069558118523922481152

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 120 1450 15100 161678 1769976 19478618 214359740 2358099550 25938154680

Decomposition

1.11.ag $\times$ 1.11.ae 2

Base change

This is a primitive isogeny class.