Properties

Label 2.193.abx_bly
Base Field $\F_{193}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{193}$
Dimension:  $2$
L-polynomial:  $( 1 - 25 x + 193 x^{2} )( 1 - 24 x + 193 x^{2} )$
Frobenius angles:  $\pm0.143734387197$, $\pm0.168091317575$
Angle rank:  $2$ (numerical)
Jacobians:  0

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 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
$A(\F_{q^r})$ 28730 1371627660 51674805040040 1925200343504505600 71709323698739690262650 2671086415201895625989483520 99495248762015167506016716216410 3706098391120093900659306841392000000 138048458708306044259547977613766040999720 5142167038111807181363297901318248242469868300

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36821 7187980 1387543777 267786748225 51682567977794 9974730695487745 1925122956692561473 371548729935091276780 71708904873095410243061

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The isogeny class factors as 1.193.az $\times$ 1.193.ay 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.ab_aig$2$(not in LMFDB)
2.193.b_aig$2$(not in LMFDB)
2.193.bx_bly$2$(not in LMFDB)
2.193.aw_na$3$(not in LMFDB)
2.193.ab_agk$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.ab_aig$2$(not in LMFDB)
2.193.b_aig$2$(not in LMFDB)
2.193.bx_bly$2$(not in LMFDB)
2.193.aw_na$3$(not in LMFDB)
2.193.ab_agk$3$(not in LMFDB)
2.193.abn_bci$4$(not in LMFDB)
2.193.al_bk$4$(not in LMFDB)
2.193.l_bk$4$(not in LMFDB)
2.193.bn_bci$4$(not in LMFDB)
2.193.abv_bkc$6$(not in LMFDB)
2.193.aba_qs$6$(not in LMFDB)
2.193.b_agk$6$(not in LMFDB)
2.193.w_na$6$(not in LMFDB)
2.193.ba_qs$6$(not in LMFDB)
2.193.bv_bkc$6$(not in LMFDB)
2.193.abl_bbg$12$(not in LMFDB)
2.193.aq_py$12$(not in LMFDB)
2.193.am_nu$12$(not in LMFDB)
2.193.aj_cm$12$(not in LMFDB)
2.193.j_cm$12$(not in LMFDB)
2.193.m_nu$12$(not in LMFDB)
2.193.q_py$12$(not in LMFDB)
2.193.bl_bbg$12$(not in LMFDB)