# Properties

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

## 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:

• $y^2=120x^6+23x^5+24x^4+138x^3+171x^2+103x+137$
• $y^2=75x^6+58x^5+93x^4+169x^3+63x^2+90x+20$
• $y^2=79x^6+49x^5+77x^4+19x^3+98x^2+97x+119$
• $y^2=108x^6+148x^5+117x^4+44x^3+125x^2+178x+1$
• $y^2=66x^6+147x^5+187x^4+82x^3+191x^2+186x+87$
• $y^2=22x^6+192x^5+35x^4+153x^3+167x^2+32x+45$
• $y^2=30x^6+158x^5+47x^4+7x^3+152x^2+140x+7$
• $y^2=156x^6+101x^5+87x^4+49x^3+97x^2+190x+132$
• $y^2=116x^6+138x^5+41x^4+64x^3+27x^2+169x+31$
• $y^2=60x^6+125x^5+163x^4+12x^3+133x^2+58x+184$
• $y^2=118x^6+155x^5+145x^4+33x^3+17x^2+99x+186$
• $y^2=157x^6+31x^5+134x^4+114x^3+26x^2+155x+44$
• $y^2=173x^6+172x^5+113x^4+184x^3+134x^2+4x+60$
• $y^2=119x^6+127x^5+12x^4+139x^3+56x^2+186x+174$
• $y^2=175x^6+184x^5+54x^4+158x^3+135x^2+90x+52$
• $y^2=55x^6+75x^5+63x^4+126x^3+25x^2+99x+4$
• $y^2=105x^6+48x^5+57x^4+176x^3+63x^2+93x+41$
• $y^2=161x^6+30x^5+26x^4+68x^3+90x^2+159x+149$
• $y^2=43x^6+80x^5+86x^4+77x^3+165x^2+101x+55$
• $y^2=114x^6+65x^5+34x^4+7x^3+50x^2+54x+91$
• $y^2=169x^6+72x^5+54x^4+77x^3+116x^2+36x+44$
• $y^2=21x^6+31x^5+65x^4+77x^3+51x^2+164x+28$
• $y^2=155x^6+65x^5+87x^4+157x^3+131x^2+61x+123$
• $y^2=57x^6+75x^5+26x^4+28x^3+52x^2+104x+30$
• $y^2=153x^6+45x^5+49x^3+9x^2+45x+175$
• $y^2=15x^6+28x^5+53x^4+104x^3+48x^2+107x+32$
• $y^2=119x^6+33x^5+146x^4+87x^3+16x^2+181x+170$

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

 $r$ 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.
 Twist Extension Degree Common 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)