# Properties

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

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## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28730 1371627660 51674805040040 1925200343504505600 71709323698739690262650 2671086415201895625989483520 99495248762015167506016716216410 3706098391120093900659306841392000000 138048458708306044259547977613766040999720 5142167038111807181363297901318248242469868300

 $r$ 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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)