Properties

Label 3.16.as_ft_abcq
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:  $( 1 - 4 x )^{2}( 1 - 7 x + 16 x^{2} )( 1 - 3 x + 16 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.160861246510$, $\pm0.377642706461$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 1260 15120000 68406746940 280166402880000 1150395290605291500 4720805152607915280000 19343659154620653400550940 79229657678272771737150720000 324517256439938287898447756326860 1329222676876905031671328436250000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 231 4079 65231 1046279 16771671 268447199 4295048351 68719202039 1099507228071

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.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.am_ch_aii$2$(not in LMFDB)
3.16.ae_af_bo$2$(not in LMFDB)
3.16.ac_al_ea$2$(not in LMFDB)
3.16.c_al_aea$2$(not in LMFDB)
3.16.e_af_abo$2$(not in LMFDB)
3.16.m_ch_ii$2$(not in LMFDB)
3.16.s_ft_bcq$2$(not in LMFDB)
3.16.ag_bd_aee$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.am_ch_aii$2$(not in LMFDB)
3.16.ae_af_bo$2$(not in LMFDB)
3.16.ac_al_ea$2$(not in LMFDB)
3.16.c_al_aea$2$(not in LMFDB)
3.16.e_af_abo$2$(not in LMFDB)
3.16.m_ch_ii$2$(not in LMFDB)
3.16.s_ft_bcq$2$(not in LMFDB)
3.16.ag_bd_aee$3$(not in LMFDB)
3.16.ak_cr_ami$4$(not in LMFDB)
3.16.ae_bb_aey$4$(not in LMFDB)
3.16.e_bb_ey$4$(not in LMFDB)
3.16.k_cr_mi$4$(not in LMFDB)
3.16.ao_ef_aum$6$(not in LMFDB)
3.16.ai_br_agq$6$(not in LMFDB)
3.16.a_l_adg$6$(not in LMFDB)
3.16.a_l_dg$6$(not in LMFDB)
3.16.g_bd_ee$6$(not in LMFDB)
3.16.i_br_gq$6$(not in LMFDB)
3.16.o_ef_um$6$(not in LMFDB)