Properties

Label 3.16.ax_iq_abto
Base Field $\F_{2^{4}}$
Dimension $3$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $3$
L-polynomial:  $( 1 - 4 x )^{4}( 1 - 7 x + 16 x^{2} )$
Frobenius angles:  $0$, $0$, $0$, $0$, $\pm0.160861246510$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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
$A(\F_{q^r})$ 810 12150000 64429610490 278049761100000 1150257900970010250 4720046579850542850000 19340269237143852590462490 79224827362032043628645400000 324514006504456338488872440778410 1329222076797878890353805830468750000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 176 3834 64736 1046154 16768976 268400154 4294786496 68718513834 1099506731696

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ai 2 $\times$ 1.16.ah 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_a_ge$2$(not in LMFDB)
3.16.ah_aq_iq$2$(not in LMFDB)
3.16.h_aq_aiq$2$(not in LMFDB)
3.16.j_a_age$2$(not in LMFDB)
3.16.x_iq_bto$2$(not in LMFDB)
3.16.al_bs_aey$3$(not in LMFDB)
3.16.b_i_adc$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.aj_a_ge$2$(not in LMFDB)
3.16.ah_aq_iq$2$(not in LMFDB)
3.16.h_aq_aiq$2$(not in LMFDB)
3.16.j_a_age$2$(not in LMFDB)
3.16.x_iq_bto$2$(not in LMFDB)
3.16.al_bs_aey$3$(not in LMFDB)
3.16.b_i_adc$3$(not in LMFDB)
3.16.ap_ea_asm$4$(not in LMFDB)
3.16.ah_bw_aiq$4$(not in LMFDB)
3.16.ab_ai_abg$4$(not in LMFDB)
3.16.b_ai_bg$4$(not in LMFDB)
3.16.h_bw_iq$4$(not in LMFDB)
3.16.p_ea_sm$4$(not in LMFDB)
3.16.ad_e_q$5$(not in LMFDB)
3.16.at_gi_abga$6$(not in LMFDB)
3.16.ap_eq_awu$6$(not in LMFDB)
3.16.ah_bg_aei$6$(not in LMFDB)
3.16.af_ae_cm$6$(not in LMFDB)
3.16.ad_am_ey$6$(not in LMFDB)
3.16.ab_i_dc$6$(not in LMFDB)
3.16.d_am_aey$6$(not in LMFDB)
3.16.f_ae_acm$6$(not in LMFDB)
3.16.h_bg_ei$6$(not in LMFDB)
3.16.l_bs_ey$6$(not in LMFDB)
3.16.p_eq_wu$6$(not in LMFDB)
3.16.t_gi_bga$6$(not in LMFDB)
3.16.ah_q_a$8$(not in LMFDB)
3.16.h_q_a$8$(not in LMFDB)
3.16.al_ci_ajg$10$(not in LMFDB)
3.16.d_e_aq$10$(not in LMFDB)
3.16.l_ci_jg$10$(not in LMFDB)
3.16.al_cy_ano$12$(not in LMFDB)
3.16.ah_a_ei$12$(not in LMFDB)
3.16.ad_u_ads$12$(not in LMFDB)
3.16.d_u_ds$12$(not in LMFDB)
3.16.h_a_aei$12$(not in LMFDB)
3.16.l_cy_no$12$(not in LMFDB)