Properties

Label 3.16.ar_fg_azv
Base Field $\F_{2^{4}}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $3$
L-polynomial:  $1 - 17 x + 136 x^{2} - 671 x^{3} + 2176 x^{4} - 4352 x^{5} + 4096 x^{6}$
Frobenius angles:  $\pm0.0601430340549$, $\pm0.180583045112$, $\pm0.403196153073$
Angle rank:  $3$ (numerical)
Number field:  6.0.1181001679.1
Galois group:  $S_4\times C_2$

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1369 15673681 68892240391 280531131810949 1151500162121819059 4723038312978021205975 19345830510758843885549256 79230273380807465800186921669 324516950189284227808824544255999 1329224189484376272149438726803914571

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 240 4107 65316 1047285 16779603 268477328 4295081724 68719137186 1099508479275

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 6.0.1181001679.1.
All geometric endomorphisms are defined over $\F_{2^{4}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.r_fg_zv$2$(not in LMFDB)