Properties

Label 2.163.aby_bkp
Base Field $\F_{163}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{163}$
Dimension:  $2$
L-polynomial:  $( 1 - 25 x + 163 x^{2} )^{2}$
Frobenius angles:  $\pm0.0652307277549$, $\pm0.0652307277549$
Angle rank:  $1$ (numerical)
Jacobians:  2

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains the Jacobians of 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 19321 690165441 18725940713104 498260220088499001 13239554876288343679561 351763779282648898653686016 9346014648606910149640314343249 248314265736217549195510067913275625 6597461724572951880052841378186437791376 175287960541966610007672298774685592764750721

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 114 25972 4323948 705839236 115062912294 18755363780998 3057125211164418 498311414511757828 81224760543592981524 13239635967230078250772

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The isogeny class factors as 1.163.az 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$
All geometric endomorphisms are defined over $\F_{163}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.163.a_aln$2$(not in LMFDB)
2.163.by_bkp$2$(not in LMFDB)
2.163.ar_ew$3$(not in LMFDB)
2.163.ai_adv$3$(not in LMFDB)
2.163.q_pa$3$(not in LMFDB)
2.163.z_ru$3$(not in LMFDB)
2.163.bi_xr$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.163.a_aln$2$(not in LMFDB)
2.163.by_bkp$2$(not in LMFDB)
2.163.ar_ew$3$(not in LMFDB)
2.163.ai_adv$3$(not in LMFDB)
2.163.q_pa$3$(not in LMFDB)
2.163.z_ru$3$(not in LMFDB)
2.163.bi_xr$3$(not in LMFDB)
2.163.a_ln$4$(not in LMFDB)
2.163.abq_bcx$6$(not in LMFDB)
2.163.abi_xr$6$(not in LMFDB)
2.163.abh_ug$6$(not in LMFDB)
2.163.az_ru$6$(not in LMFDB)
2.163.aq_pa$6$(not in LMFDB)
2.163.aj_hi$6$(not in LMFDB)
2.163.a_bl$6$(not in LMFDB)
2.163.a_kc$6$(not in LMFDB)
2.163.i_adv$6$(not in LMFDB)
2.163.j_hi$6$(not in LMFDB)
2.163.r_ew$6$(not in LMFDB)
2.163.bh_ug$6$(not in LMFDB)
2.163.bq_bcx$6$(not in LMFDB)
2.163.a_akc$12$(not in LMFDB)
2.163.a_abl$12$(not in LMFDB)