Properties

Label 3.3.ae_l_aw
Base Field $\F_{3}$
Dimension $3$
$p$-rank $3$

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $1 - 4 x + 11 x^{2} - 22 x^{3} + 33 x^{4} - 36 x^{5} + 27 x^{6}$
Frobenius angles:  $\pm0.132091637252$, $\pm0.376445424065$, $\pm0.544359499442$
Angle rank:  $3$ (numerical)
Number field:  6.0.5169344.1
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

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 10 1340 22030 455600 14700050 410330780 10709109190 293340793600 7859863377970 205846769956700

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 16 30 68 250 772 2240 6812 20280 59036

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.