Properties

Label 3.4.ag_v_abx
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:  $1 - 6 x + 21 x^{2} - 49 x^{3} + 84 x^{4} - 96 x^{5} + 64 x^{6}$
Frobenius angles:  $\pm0.155504948432$, $\pm0.300378009331$, $\pm0.490400327376$
Angle rank:  $3$ (numerical)
Number field:  6.0.3877551.1
Galois group:  The Galois group of this isogeny class is not in the database.

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
$A(\F_{q^r})$ 19 6099 337573 17132091 1117367029 71193132981 4413174983488 280265949652011 18059531552684191 1156941846161126709

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 23 80 263 1064 4244 16442 65255 262799 1052228

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.