Properties

Label 3.9.am_ct_akd
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:  $1 - 12 x + 71 x^{2} - 263 x^{3} + 639 x^{4} - 972 x^{5} + 729 x^{6}$
Frobenius angles:  $\pm0.0686978556945$, $\pm0.249138957169$, $\pm0.398269757982$
Angle rank:  $3$ (numerical)
Number field:  6.0.50290919.1
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
$A(\F_{q^r})$ 193 518591 408369472 282860793631 204613810823888 149850143758896896 109422255871771699049 79766179137142637449999 58146055380774870679756096 42390481504598478783681062656

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 80 769 6572 58683 530573 4783112 43046580 387395959 3486728735

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.