Properties

Label 3.9.am_ct_akc
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:  $1 - 12 x + 71 x^{2} - 262 x^{3} + 639 x^{4} - 972 x^{5} + 729 x^{6}$
Frobenius angles:  $\pm0.105225994061$, $\pm0.226892402608$, $\pm0.403809371059$
Angle rank:  $3$ (numerical)
Number field:  6.0.41968064.1
Galois group:  The Galois group of this isogeny class is not in the database.

This isogeny class is simple.

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
$A(\F_{q^r})$ 194 521084 410719922 284972502256 205881813170354 150335516509876316 109544986261457040418 79785703718873415188224 58147287323211478481267186 42390196082299608875189516284

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 80 772 6620 59048 532292 4788474 43057116 387404170 3486705260

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.