Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $1 - 2 x + 3 x^{2} - 6 x^{3} + 6 x^{4} - 8 x^{5} + 8 x^{6}$
Frobenius angles:  $\pm0.0325998547649$, $\pm0.44007765443$, $\pm0.657477799665$
Angle rank:  $2$ (numerical)
Number field:  6.0.399424.1
Galois group:  $S_3\times C_2$

This isogeny class is simple.

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2 68 146 2176 22082 183668 2299978 16720384 106675922 1036838228

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 7 1 7 21 43 141 255 397 987

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.