Properties

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

Learn more about

Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $3$
L-polynomial:  $( 1 - 7 x + 16 x^{2} )( 1 - 11 x + 59 x^{2} - 176 x^{3} + 256 x^{4} )$
Frobenius angles:  $\pm0.133878927982$, $\pm0.160861246510$, $\pm0.347077071791$
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
$A(\F_{q^r})$ 1290 15572880 70106706360 283450491672480 1154387250938439750 4724308729222887502080 19346788887818584636774290 79233867618048694791564160320 324523229897252273700668224313160 1329228609704534125081791858230082000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 237 4178 65993 1049909 16784118 268490627 4295276561 68720466962 1099512135597

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ah $\times$ 2.16.al_ch 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_ac_cj$2$(not in LMFDB)
3.16.e_ac_acj$2$(not in LMFDB)
3.16.s_fw_bdl$2$(not in LMFDB)