Properties

Label 3.16.as_fu_abcx
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:  $( 1 - 7 x + 16 x^{2} )( 1 - 11 x + 57 x^{2} - 176 x^{3} + 256 x^{4} )$
Frobenius angles:  $\pm0.0728689886706$, $\pm0.160861246510$, $\pm0.368631800070$
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
$A(\F_{q^r})$ 1270 15270480 68971993120 281276896932000 1151846432542081750 4722392578368749184000 19345656943985097319360630 79232673095668668222155592000 324521464240277940063829139426080 1329227415473205395064169597044762000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 233 4112 65489 1047599 16777310 268474919 4295211809 68720093072 1099511147753

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ah $\times$ 2.16.al_cf 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.ae_ae_bv$2$(not in LMFDB)
3.16.e_ae_abv$2$(not in LMFDB)
3.16.s_fu_bcx$2$(not in LMFDB)