Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $1 - 2 x + 3 x^{2} - 5 x^{3} + 6 x^{4} - 8 x^{5} + 8 x^{6}$
Frobenius angles:  $\pm0.0964297006873$, $\pm0.413303350042$, $\pm0.672715745192$
Angle rank:  $3$ (numerical)
Number field:  6.0.3194271.1
Galois group:  $S_4\times C_2$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3 99 243 4059 26763 216513 3024024 20786139 125737191 1122520509

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 7 4 15 26 52 176 311 481 1072

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.