Properties

Label 3.4.ag_u_abv
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:  $1 - 6 x + 20 x^{2} - 47 x^{3} + 80 x^{4} - 96 x^{5} + 64 x^{6}$
Frobenius angles:  $\pm0.0842195913666$, $\pm0.309444685979$, $\pm0.509145309743$
Angle rank:  $3$ (numerical)
Number field:  6.0.10016231.1
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
$A(\F_{q^r})$ 16 5024 275776 15242816 1059997936 68928556544 4344490094128 280311514564736 18138768217237312 1159229869618198304

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 21 68 233 1009 4110 16183 65265 263948 1054301

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.