Properties

Label 3.9.aq_ei_aqw
Base Field $\F_{3^2}$
Dimension $3$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x )^{2}( 1 - 5 x + 9 x^{2} )^{2}$
Frobenius angles:  $0.0$, $0.0$, $\pm0.186429498677$, $\pm0.186429498677$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 100 360000 370177600 285156000000 207505465502500 150449653186560000 109433989938549444100 79743441142771344000000 58137564683082125258305600 42387108089992314093225000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 50 696 6626 59514 532700 4783626 43034306 387339384 3486451250

Decomposition

1.9.ag $\times$ 1.9.af 2

Base change

This is a primitive isogeny class.