Properties

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

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 5 x + 9 x^{2} )^{3}$
Frobenius angles:  $\pm0.186429498677$, $\pm0.186429498677$, $\pm0.186429498677$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 125 421875 405224000 297408796875 210910505328125 151249047552000000 109591754009143959125 79768411000496443546875 58140340534381421625128000 42387236600747445797607421875

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 61 760 6901 60475 535516 4790515 43047781 387357880 3486461821

Decomposition

1.9.af 3

Base change

This is a primitive isogeny class.