Properties

Label 3.16.as_fy_abeb
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:  $( 1 - 5 x + 16 x^{2} )( 1 - 13 x + 73 x^{2} - 208 x^{3} + 256 x^{4} )$
Frobenius angles:  $\pm0.0987587980325$, $\pm0.265114785720$, $\pm0.285098958592$
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
$A(\F_{q^r})$ 1308 15855576 71115829200 284928664614000 1154576739593228268 4720963516839107366400 19339664506865473444061268 79226291284220673300792876000 324520521294602466159155249425200 1329233950849567605986035787678097336

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 241 4238 66337 1050079 16772230 268391759 4294865857 68719893398 1099516553681

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.af $\times$ 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.ai_y_abz$2$(not in LMFDB)
3.16.i_y_bz$2$(not in LMFDB)
3.16.s_fy_beb$2$(not in LMFDB)