Properties

Label 3.3.af_n_az
Base Field $\F_{3}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $1-5x+13x^{2}-25x^{3}+39x^{4}-45x^{5}+27x^{6}$
Frobenius angles:  $\pm0.0714477711956$, $\pm0.27207177608$, $\pm0.560185743604$
Angle rank:  $3$ (numerical)
Number field:  6.0.1342367.1
Galois group:  $A_4\times C_2$

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
$A(\F_{q^r})$ 5 775 16355 484375 15965275 382788775 9630701120 277752734375 7764618989945 207509060944375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 11 23 75 269 719 2008 6451 20039 59511

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.