Properties

Label 3.16.au_gy_abjr
Base Field $\F_{2^{4}}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $3$
L-polynomial:  $( 1 - 7 x + 16 x^{2} )( 1 - 13 x + 73 x^{2} - 208 x^{3} + 256 x^{4} )$
Frobenius angles:  $\pm0.0987587980325$, $\pm0.160861246510$, $\pm0.265114785720$
Angle rank:  $3$ (numerical)

This isogeny class is not 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 does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1090 14414160 69055969000 283892560379040 1155895247097177250 4724672241671715456000 19344203806287267287679010 79229328343334966979423600960 324520417014837036820015674721000 1329230839907278291474161111114234000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 217 4116 66097 1051277 16785406 268454757 4295030497 68719871316 1099513980377

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ah $\times$ 2.16.an_cv and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ag_ac_dr$2$(not in LMFDB)
3.16.g_ac_adr$2$(not in LMFDB)
3.16.u_gy_bjr$2$(not in LMFDB)