Properties

Label 3.16.as_fy_abdz
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:  $( 1 - 7 x + 16 x^{2} )( 1 - 11 x + 61 x^{2} - 176 x^{3} + 256 x^{4} )$
Frobenius angles:  $\pm0.160861246510$, $\pm0.189901625224$, $\pm0.315486115946$
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
$A(\F_{q^r})$ 1310 15877200 71247211040 285561508144800 1156447080670947750 4724569989308567116800 19344325050557845649323790 79229698519641229741356667200 324519613489855317296518828096160 1329226979735629708856794148906250000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 241 4244 66481 1051779 16785046 268456439 4295050561 68719701164 1099510787321

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ah $\times$ 2.16.al_cj 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_a_cx$2$(not in LMFDB)
3.16.e_a_acx$2$(not in LMFDB)
3.16.s_fy_bdz$2$(not in LMFDB)