Properties

Label 3.11.ao_dp_aoq
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:  $( 1 - 2 x + 11 x^{2} )( 1 - 6 x + 11 x^{2} )^{2}$
Frobenius angles:  $\pm0.140218899004$, $\pm0.140218899004$, $\pm0.402508885479$
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
$A(\F_{q^r})$ 360 1632960 2399968440 3141135728640 4181026450329000 5572402721940600000 7409766361514515019640 9853266309353470175477760 13110525746317059899073494760 17449317334841144616690201144000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 112 1354 14652 161198 1775536 19512218 214435772 2358043294 25937298352

Decomposition

1.11.ag 2 $\times$ 1.11.ac

Base change

This is a primitive isogeny class.