Properties

Label 3.16.at_ge_abeu
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:  $( 1 - 4 x )^{4}( 1 - 3 x + 16 x^{2} )$
Frobenius angles:  $0$, $0$, $0$, $0$, $\pm0.377642706461$
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
$A(\F_{q^r})$ 1134 14175000 66382977654 277034980950000 1146319479249574014 4716211009130036325000 19339119766848606045878214 79225739313395830480716300000 324514375995661382014727289471054 1329220989977712956601982041796875000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 216 3958 64496 1042558 16755336 268384198 4294835936 68718592078 1099505832696

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ai 2 $\times$ 1.16.ad 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.an_cm_aiq$2$(not in LMFDB)
3.16.ad_aq_ds$2$(not in LMFDB)
3.16.d_aq_ads$2$(not in LMFDB)
3.16.n_cm_iq$2$(not in LMFDB)
3.16.t_ge_beu$2$(not in LMFDB)
3.16.ah_bc_aey$3$(not in LMFDB)
3.16.f_bo_ei$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.an_cm_aiq$2$(not in LMFDB)
3.16.ad_aq_ds$2$(not in LMFDB)
3.16.d_aq_ads$2$(not in LMFDB)
3.16.n_cm_iq$2$(not in LMFDB)
3.16.t_ge_beu$2$(not in LMFDB)
3.16.ah_bc_aey$3$(not in LMFDB)
3.16.f_bo_ei$3$(not in LMFDB)
3.16.al_cu_ano$4$(not in LMFDB)
3.16.af_y_age$4$(not in LMFDB)
3.16.ad_bw_ads$4$(not in LMFDB)
3.16.d_bw_ds$4$(not in LMFDB)
3.16.f_y_ge$4$(not in LMFDB)
3.16.l_cu_no$4$(not in LMFDB)
3.16.b_u_dc$5$(not in LMFDB)
3.16.ap_em_awe$6$(not in LMFDB)
3.16.al_dk_apk$6$(not in LMFDB)
3.16.aj_bs_ahk$6$(not in LMFDB)
3.16.af_bo_aei$6$(not in LMFDB)
3.16.ad_bg_abw$6$(not in LMFDB)
3.16.ab_e_aey$6$(not in LMFDB)
3.16.b_e_ey$6$(not in LMFDB)
3.16.d_bg_bw$6$(not in LMFDB)
3.16.h_bc_ey$6$(not in LMFDB)
3.16.j_bs_hk$6$(not in LMFDB)
3.16.l_dk_pk$6$(not in LMFDB)
3.16.p_em_we$6$(not in LMFDB)
3.16.ad_q_a$8$(not in LMFDB)
3.16.d_q_a$8$(not in LMFDB)
3.16.ah_bs_agu$10$(not in LMFDB)
3.16.ab_u_adc$10$(not in LMFDB)
3.16.h_bs_gu$10$(not in LMFDB)
3.16.ah_ci_aiq$12$(not in LMFDB)
3.16.ad_a_bw$12$(not in LMFDB)
3.16.ab_bk_abg$12$(not in LMFDB)
3.16.b_bk_bg$12$(not in LMFDB)
3.16.d_a_abw$12$(not in LMFDB)
3.16.h_ci_iq$12$(not in LMFDB)