Properties

Label 2.193.aby_bmx
Base Field $\F_{193}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{193}$
Dimension:  $2$
L-polynomial:  $( 1 - 25 x + 193 x^{2} )^{2}$
Frobenius angles:  $\pm0.143734387197$, $\pm0.143734387197$
Angle rank:  $1$ (numerical)
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28561 1369814121 51666021416464 1925171176753933641 71709256409245886243761 2671086347119640841444458496 99495249060631298608475922191089 3706098393377197138625638880066015625 138048458717533024006991211940954753144336 5142167038139989589404007356298021986465358121

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36772 7186758 1387522756 267786496944 51682566660478 9974730725425008 1925122957865007748 371548729959925111494 71708904873488421516772

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The isogeny class factors as 1.193.az 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$
All geometric endomorphisms are defined over $\F_{193}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.a_ajf$2$(not in LMFDB)
2.193.by_bmx$2$(not in LMFDB)
2.193.ax_my$3$(not in LMFDB)
2.193.ac_ahh$3$(not in LMFDB)
2.193.e_pa$3$(not in LMFDB)
2.193.z_qq$3$(not in LMFDB)
2.193.bu_bjf$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.a_ajf$2$(not in LMFDB)
2.193.by_bmx$2$(not in LMFDB)
2.193.ax_my$3$(not in LMFDB)
2.193.ac_ahh$3$(not in LMFDB)
2.193.e_pa$3$(not in LMFDB)
2.193.z_qq$3$(not in LMFDB)
2.193.bu_bjf$3$(not in LMFDB)
2.193.a_jf$4$(not in LMFDB)
2.193.abw_bkz$6$(not in LMFDB)
2.193.abu_bjf$6$(not in LMFDB)
2.193.abb_qu$6$(not in LMFDB)
2.193.az_qq$6$(not in LMFDB)
2.193.av_nc$6$(not in LMFDB)
2.193.ae_pa$6$(not in LMFDB)
2.193.a_afn$6$(not in LMFDB)
2.193.a_os$6$(not in LMFDB)
2.193.c_ahh$6$(not in LMFDB)
2.193.v_nc$6$(not in LMFDB)
2.193.x_my$6$(not in LMFDB)
2.193.bb_qu$6$(not in LMFDB)
2.193.bw_bkz$6$(not in LMFDB)
2.193.a_aos$12$(not in LMFDB)
2.193.a_fn$12$(not in LMFDB)