Properties

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

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $3$
L-polynomial:  $( 1 - 4 x )^{2}( 1 - 9 x + 43 x^{2} - 144 x^{3} + 256 x^{4} )$
Frobenius angles:  $0$, $0$, $\pm0.108303609292$, $\pm0.441636942625$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $2$
Slopes:  $[0, 0, 1/2, 1/2, 1, 1]$

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
$A(\F_{q^r})$ 1323 14982975 66603519108 277216037275275 1149181225223419773 4722152053598405571600 19344427927754309658188127 79227701795450409038033800275 324516077773744637635536636725148 1329227251536537493926963729830499375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 230 3969 64538 1045170 16776455 268457868 4294942322 68718952449 1099511012150

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ai $\times$ 2.16.aj_br and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
Endomorphism algebra over $\overline{\F}_{2^{4}}$
The base change of $A$ to $\F_{2^{24}}$ is 1.16777216.amdc $\times$ 1.16777216.fmx 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{24}}$.
Remainder of endomorphism lattice by field

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.ab_an_ce$2$(not in LMFDB)
3.16.b_an_ace$2$(not in LMFDB)
3.16.r_fb_yi$2$(not in LMFDB)
3.16.ai_l_bo$3$(not in LMFDB)
3.16.af_x_aem$3$(not in LMFDB)
3.16.e_l_au$3$(not in LMFDB)
3.16.n_dr_rs$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.ab_an_ce$2$(not in LMFDB)
3.16.b_an_ace$2$(not in LMFDB)
3.16.r_fb_yi$2$(not in LMFDB)
3.16.ai_l_bo$3$(not in LMFDB)
3.16.af_x_aem$3$(not in LMFDB)
3.16.e_l_au$3$(not in LMFDB)
3.16.n_dr_rs$3$(not in LMFDB)
3.16.aj_ch_alc$4$(not in LMFDB)
3.16.j_ch_lc$4$(not in LMFDB)
3.16.an_dr_ars$6$(not in LMFDB)
3.16.ae_l_u$6$(not in LMFDB)
3.16.f_x_em$6$(not in LMFDB)
3.16.i_l_abo$6$(not in LMFDB)
3.16.ai_v_abo$12$(not in LMFDB)
3.16.ae_v_au$12$(not in LMFDB)
3.16.a_l_a$12$(not in LMFDB)
3.16.a_v_a$12$(not in LMFDB)
3.16.e_v_u$12$(not in LMFDB)
3.16.i_v_bo$12$(not in LMFDB)