Properties

Label 3.16.as_fx_abdw
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:  $( 1 - 4 x )^{2}( 1 - 5 x + 16 x^{2} )^{2}$
Frobenius angles:  $0$, $0$, $\pm0.285098958592$, $\pm0.285098958592$
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
$A(\F_{q^r})$ 1296 15681600 70413806736 283248900000000 1151715733086598416 4717229964795458510400 19335731077125739182817296 79222671724663902243600000000 324517095502749275604122886158736 1329229985557187271158741753787240000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 239 4199 65951 1047479 16758959 268337159 4294669631 68719167959 1099513273679

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ai $\times$ 1.16.af 2 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.ai_x_ace$2$(not in LMFDB)
3.16.ac_ah_fg$2$(not in LMFDB)
3.16.c_ah_afg$2$(not in LMFDB)
3.16.i_x_ce$2$(not in LMFDB)
3.16.s_fx_bdw$2$(not in LMFDB)
3.16.ag_bh_ado$3$(not in LMFDB)
3.16.ad_ap_dk$3$(not in LMFDB)
3.16.j_bt_ho$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.ai_x_ace$2$(not in LMFDB)
3.16.ac_ah_fg$2$(not in LMFDB)
3.16.c_ah_afg$2$(not in LMFDB)
3.16.i_x_ce$2$(not in LMFDB)
3.16.s_fx_bdw$2$(not in LMFDB)
3.16.ag_bh_ado$3$(not in LMFDB)
3.16.ad_ap_dk$3$(not in LMFDB)
3.16.j_bt_ho$3$(not in LMFDB)
3.16.ak_cv_ami$4$(not in LMFDB)
3.16.ai_j_ce$4$(not in LMFDB)
3.16.a_j_a$4$(not in LMFDB)
3.16.a_x_a$4$(not in LMFDB)
3.16.i_j_ace$4$(not in LMFDB)
3.16.k_cv_mi$4$(not in LMFDB)
3.16.ao_ej_avc$6$(not in LMFDB)
3.16.an_cn_aiy$6$(not in LMFDB)
3.16.aj_bt_aho$6$(not in LMFDB)
3.16.ae_x_abc$6$(not in LMFDB)
3.16.ab_f_aeu$6$(not in LMFDB)
3.16.b_f_eu$6$(not in LMFDB)
3.16.d_ap_adk$6$(not in LMFDB)
3.16.e_x_bc$6$(not in LMFDB)
3.16.g_bh_do$6$(not in LMFDB)
3.16.n_cn_iy$6$(not in LMFDB)
3.16.o_ej_vc$6$(not in LMFDB)
3.16.af_z_age$12$(not in LMFDB)
3.16.ae_j_bc$12$(not in LMFDB)
3.16.e_j_abc$12$(not in LMFDB)
3.16.f_z_ge$12$(not in LMFDB)