Properties

Label 3.4.ag_t_abr
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:  $1 - 6 x + 19 x^{2} - 43 x^{3} + 76 x^{4} - 96 x^{5} + 64 x^{6}$
Frobenius angles:  $\pm0.0919564268332$, $\pm0.268791443494$, $\pm0.539160395357$
Angle rank:  $3$ (numerical)
Number field:  6.0.12086967.1
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
$A(\F_{q^r})$ 15 4575 252855 16090275 1139454825 69948542925 4312645821240 279787371955275 18120248060855805 1157115263819045625

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 19 62 247 1084 4168 16064 65143 263681 1052384

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.