Properties

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

Learn more about

Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $3$
L-polynomial:  $( 1 - 4 x )^{2}( 1 - 7 x + 16 x^{2} )( 1 - 4 x + 16 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.160861246510$, $\pm0.333333333333$
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
$A(\F_{q^r})$ 1170 14742000 68585312250 281333762892000 1151383396862234250 4720046579850542850000 19341449817608086929339930 79228454097498072812571672000 324518958233008035416524588142250 1329225879739998750287299160388750000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 224 4090 65504 1047178 16768976 268416538 4294983104 68719562410 1099509877424

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ai $\times$ 1.16.ah $\times$ 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 $\F_{2^{24}}$ is 1.16777216.amdc 2 $\times$ 1.16777216.mbf. 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.al_bs_aey$2$(not in LMFDB)
3.16.af_ae_cm$2$(not in LMFDB)
3.16.ad_am_ey$2$(not in LMFDB)
3.16.d_am_aey$2$(not in LMFDB)
3.16.f_ae_acm$2$(not in LMFDB)
3.16.l_bs_ey$2$(not in LMFDB)
3.16.t_gi_bga$2$(not in LMFDB)
3.16.ah_aq_iq$3$(not in LMFDB)
3.16.ah_bg_aei$3$(not in LMFDB)
3.16.f_ae_acm$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.al_bs_aey$2$(not in LMFDB)
3.16.af_ae_cm$2$(not in LMFDB)
3.16.ad_am_ey$2$(not in LMFDB)
3.16.d_am_aey$2$(not in LMFDB)
3.16.f_ae_acm$2$(not in LMFDB)
3.16.l_bs_ey$2$(not in LMFDB)
3.16.t_gi_bga$2$(not in LMFDB)
3.16.ah_aq_iq$3$(not in LMFDB)
3.16.ah_bg_aei$3$(not in LMFDB)
3.16.f_ae_acm$3$(not in LMFDB)
3.16.al_cy_ano$4$(not in LMFDB)
3.16.ad_u_ads$4$(not in LMFDB)
3.16.d_u_ds$4$(not in LMFDB)
3.16.l_cy_no$4$(not in LMFDB)
3.16.ax_iq_abto$6$(not in LMFDB)
3.16.ap_eq_awu$6$(not in LMFDB)
3.16.aj_a_ge$6$(not in LMFDB)
3.16.ab_i_dc$6$(not in LMFDB)
3.16.b_i_adc$6$(not in LMFDB)
3.16.h_aq_aiq$6$(not in LMFDB)
3.16.h_bg_ei$6$(not in LMFDB)
3.16.j_a_age$6$(not in LMFDB)
3.16.p_eq_wu$6$(not in LMFDB)
3.16.x_iq_bto$6$(not in LMFDB)
3.16.ap_ea_asm$12$(not in LMFDB)
3.16.ah_a_ei$12$(not in LMFDB)
3.16.ah_bw_aiq$12$(not in LMFDB)
3.16.ab_ai_abg$12$(not in LMFDB)
3.16.b_ai_bg$12$(not in LMFDB)
3.16.h_a_aei$12$(not in LMFDB)
3.16.h_bw_iq$12$(not in LMFDB)
3.16.p_ea_sm$12$(not in LMFDB)
3.16.ah_q_a$24$(not in LMFDB)
3.16.h_q_a$24$(not in LMFDB)
3.16.al_ci_ajg$30$(not in LMFDB)
3.16.ad_e_q$30$(not in LMFDB)
3.16.d_e_aq$30$(not in LMFDB)
3.16.l_ci_jg$30$(not in LMFDB)