Properties

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

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $1 - 2 x + 2 x^{2} - x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6}$
Frobenius angles:  $\pm0.16133478918$, $\pm0.327009058845$, $\pm0.739882802642$
Angle rank:  $3$ (numerical)
Number field:  6.0.2464727.1
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
$A(\F_{q^r})$ 4 104 592 11024 31604 246272 2553436 16778528 154949488 1118339144

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 5 10 33 31 62 155 257 586 1065

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.