Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6}$
Frobenius angles:  $\pm0.147012170705$, $\pm0.34196271642$, $\pm0.600633654388$
Angle rank:  $3$ (numerical)
Number field:  6.0.465831.1
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

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3 153 513 5661 46923 235467 2042904 22423221 157333509 1031414463

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 8 9 20 45 59 126 332 594 983

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.