Properties

Label 3.16.av_hl_abmm
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:  $( 1 - 4 x )^{2}( 1 - 13 x + 73 x^{2} - 208 x^{3} + 256 x^{4} )$
Frobenius angles:  $0$, $0$, $\pm0.0987587980325$, $\pm0.265114785720$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 981 13513275 67012992900 280719491159475 1151799949582824861 4720074334860797640000 19339664290701495772047381 79225409994745543438690210275 324517536542506584635842405716900 1329229152997726620844881738443806875

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 202 3995 65362 1047556 16769071 268391756 4294818082 68719261355 1099512585002

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ai $\times$ 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.af_ap_gm$2$(not in LMFDB)
3.16.f_ap_agm$2$(not in LMFDB)
3.16.v_hl_bmm$2$(not in LMFDB)
3.16.aj_bl_aeu$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.af_ap_gm$2$(not in LMFDB)
3.16.f_ap_agm$2$(not in LMFDB)
3.16.v_hl_bmm$2$(not in LMFDB)
3.16.aj_bl_aeu$3$(not in LMFDB)
3.16.an_dl_aqa$4$(not in LMFDB)
3.16.n_dl_qa$4$(not in LMFDB)
3.16.ar_fl_abbg$6$(not in LMFDB)
3.16.j_bl_eu$6$(not in LMFDB)
3.16.r_fl_bbg$6$(not in LMFDB)