Properties

Label 3.4.ah_ba_acl
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $1 - 7 x + 26 x^{2} - 63 x^{3} + 104 x^{4} - 112 x^{5} + 64 x^{6}$
Frobenius angles:  $\pm0.10058761729$, $\pm0.290662784222$, $\pm0.439716826337$
Angle rank:  $3$ (numerical)
Number field:  6.0.573839.1
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

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13 4901 326677 16472261 1032240313 68844891011 4437256066984 282008551022549 18036949300358521 1156618444511310131

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 20 79 252 983 4103 16532 65660 262474 1051935

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.