Properties

Label 3.2.ac_c_ac
Base Field $\F_{2}$
Dimension $3$
$p$-rank $0$

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $1 - 2 x + 2 x^{2} - 2 x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6}$
Frobenius angles:  $\pm0.111901318694$, $\pm0.359194778829$, $\pm0.729359314356$
Angle rank:  $3$ (numerical)
Number field:  6.0.1142512.1
Galois group:  $S_4\times C_2$

This isogeny class is simple.

Newton polygon

$p$-rank:  $0$
Slopes:  $[1/3, 1/3, 1/3, 2/3, 2/3, 2/3]$

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3 81 387 7209 23493 219429 2866377 18865953 159327513 1161423441

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 5 7 25 21 53 169 289 601 1105

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.