Properties

Label 3.9.an_dd_alt
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:  $1 - 13 x + 81 x^{2} - 305 x^{3} + 729 x^{4} - 1053 x^{5} + 729 x^{6}$
Frobenius angles:  $\pm0.0820148229506$, $\pm0.234427519578$, $\pm0.348266280931$
Angle rank:  $3$ (numerical)
Number field:  6.0.2590679.1
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
$A(\F_{q^r})$ 169 491959 412836073 288052325639 205707924181409 149808520390558471 109379841389054919488 79774449678535285605191 58153585802887725433128313 42391774358761564365133447319

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 75 777 6691 58997 530427 4781256 43051043 387446133 3486835075

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.