Properties

Label 3.9.as_ff_auu
Base Field $\F_{3^2}$
Dimension $3$
$p$-rank $0$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $(1-3x)^{6}$
Frobenius angles:  $0.0$, $0.0$, $0.0$, $0.0$, $0.0$, $0.0$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 64 262144 308915776 262144000000 200859416110144 148863517207035904 109119142803669852736 79693524873773056000000 58132013378067778004674624 42386851069650916514275262464

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -8 28 568 6076 57592 527068 4769848 43007356 387302392 3486430108

Decomposition

1.9.ag 3

Base change

This is a primitive isogeny class.