Properties

Label 3.16.as_fx_abds
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:  $( 1 - 4 x + 16 x^{2} )( 1 - 7 x + 16 x^{2} )^{2}$
Frobenius angles:  $\pm0.160861246510$, $\pm0.160861246510$, $\pm0.333333333333$
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
$A(\F_{q^r})$ 1300 15724800 70676222500 284513775436800 1155477213297062500 4724644459624820640000 19345989752302851209755300 79232372596643431970739916800 324521838717957652024064133302500 1329227566645396366881748025028000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 239 4211 66239 1050899 16785311 268479539 4295195519 68720172371 1099511272799

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ah 2 $\times$ 1.16.ae 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 $\F_{2^{12}}$ is 1.4096.ah 2 $\times$ 1.4096.ey. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{12}}$.

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.ak_bp_aeu$2$(not in LMFDB)
3.16.ae_ab_cq$2$(not in LMFDB)
3.16.e_ab_acq$2$(not in LMFDB)
3.16.k_bp_eu$2$(not in LMFDB)
3.16.s_fx_bds$2$(not in LMFDB)
3.16.ag_ap_hs$3$(not in LMFDB)
3.16.d_v_do$3$(not in LMFDB)
3.16.p_eb_su$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.ak_bp_aeu$2$(not in LMFDB)
3.16.ae_ab_cq$2$(not in LMFDB)
3.16.e_ab_acq$2$(not in LMFDB)
3.16.k_bp_eu$2$(not in LMFDB)
3.16.s_fx_bds$2$(not in LMFDB)
3.16.ag_ap_hs$3$(not in LMFDB)
3.16.d_v_do$3$(not in LMFDB)
3.16.p_eb_su$3$(not in LMFDB)
3.16.ae_bh_acq$4$(not in LMFDB)
3.16.e_bh_cq$4$(not in LMFDB)
3.16.aw_ib_abqe$6$(not in LMFDB)
3.16.ap_eb_asu$6$(not in LMFDB)
3.16.al_cz_ans$6$(not in LMFDB)
3.16.ai_ab_fg$6$(not in LMFDB)
3.16.ad_v_ado$6$(not in LMFDB)
3.16.ab_ah_abo$6$(not in LMFDB)
3.16.b_ah_bo$6$(not in LMFDB)
3.16.g_ap_ahs$6$(not in LMFDB)
3.16.i_ab_afg$6$(not in LMFDB)
3.16.l_cz_ns$6$(not in LMFDB)
3.16.s_fx_bds$6$(not in LMFDB)
3.16.w_ib_bqe$6$(not in LMFDB)
3.16.ao_dt_arg$12$(not in LMFDB)
3.16.ai_bh_afg$12$(not in LMFDB)
3.16.ah_bx_aiq$12$(not in LMFDB)
3.16.a_ab_a$12$(not in LMFDB)
3.16.a_bh_a$12$(not in LMFDB)
3.16.h_bx_iq$12$(not in LMFDB)
3.16.i_bh_fg$12$(not in LMFDB)
3.16.o_dt_rg$12$(not in LMFDB)