Properties

Label 2.193.abx_bls
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:  $( 1 - 27 x + 193 x^{2} )( 1 - 22 x + 193 x^{2} )$
Frobenius angles:  $\pm0.0758389534121$, $\pm0.209145594264$
Angle rank:  $2$ (numerical)
Jacobians:  27

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 27 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28724 1371168864 51668455909184 1925153121045338496 71709076489180543513364 2671085410342393148769540096 99495245494204664238445797681044 3706098382848084087791936218884539904 138048458694648637680509341715817344634176 5142167038115999635159902551988748953147587424

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36809 7187098 1387509745 267785825065 51682548534878 9974730367878841 1925122952395687969 371548729898333227354 71708904873153875140889

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The isogeny class factors as 1.193.abb $\times$ 1.193.aw 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 $\F_{193}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.af_aia$2$(not in LMFDB)
2.193.f_aia$2$(not in LMFDB)
2.193.bx_bls$2$(not in LMFDB)