Properties

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

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $1 - 6 x + 17 x^{2} - 35 x^{3} + 68 x^{4} - 96 x^{5} + 64 x^{6}$
Frobenius angles:  $\pm0.12572512263$, $\pm0.183009650264$, $\pm0.584457690022$
Angle rank:  $3$ (numerical)
Number field:  6.0.400967.1
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 3731 213109 17285723 1240653973 72354980789 4439477133832 285099116441867 18095807585396437 1150551201545039021

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 15 50 263 1174 4308 16540 66375 263327 1046420

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.