Properties

Label 3.16.at_gl_abgv
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:  $( 1 - 5 x + 16 x^{2} )( 1 - 7 x + 16 x^{2} )^{2}$
Frobenius angles:  $\pm0.160861246510$, $\pm0.160861246510$, $\pm0.285098958592$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 1200 15206400 70458757200 285408921600000 1157130647865750000 4725534502537151846400 19344809110947560958061200 79229627008386207993446400000 324519871691574786700836054385200 1329228561530838549088135276704000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 230 4198 66446 1052398 16788470 268463158 4295046686 68719755838 1099512095750

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ah 2 $\times$ 1.16.af 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.aj_bb_abr$2$(not in LMFDB)
3.16.af_ab_dh$2$(not in LMFDB)
3.16.f_ab_adh$2$(not in LMFDB)
3.16.j_bb_br$2$(not in LMFDB)
3.16.t_gl_bgv$2$(not in LMFDB)
3.16.c_o_ch$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.aj_bb_abr$2$(not in LMFDB)
3.16.af_ab_dh$2$(not in LMFDB)
3.16.f_ab_adh$2$(not in LMFDB)
3.16.j_bb_br$2$(not in LMFDB)
3.16.t_gl_bgv$2$(not in LMFDB)
3.16.c_o_ch$3$(not in LMFDB)
3.16.af_bh_adh$4$(not in LMFDB)
3.16.f_bh_dh$4$(not in LMFDB)
3.16.am_dg_aoz$6$(not in LMFDB)
3.16.ac_o_ach$6$(not in LMFDB)
3.16.m_dg_oz$6$(not in LMFDB)