# Properties

 Label 2.193.abv_bjn 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: $1 - 47 x + 923 x^{2} - 9071 x^{3} + 37249 x^{4}$ Frobenius angles: $\pm0.0526881694498$, $\pm0.250841491310$ Angle rank: $2$ (numerical) Number field: 4.0.30262893.1 Galois group: $D_{4}$ Jacobians: 26

This isogeny class is simple and geometrically 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 26 curves, and hence is principally polarizable:

• $y^2=12x^6+86x^5+27x^4+72x^3+36x^2+124x+42$
• $y^2=167x^6+85x^5+51x^4+8x^3+122x^2+15x+183$
• $y^2=82x^6+106x^5+112x^4+115x^3+89x^2+64x+21$
• $y^2=155x^6+85x^5+9x^4+133x^3+105x^2+103x+119$
• $y^2=39x^6+18x^5+38x^4+132x^3+150x^2+131x+160$
• $y^2=181x^6+43x^5+176x^4+50x^3+165x^2+126x+17$
• $y^2=104x^6+116x^5+190x^4+14x^3+34x^2+125x+160$
• $y^2=80x^6+54x^5+23x^4+155x^3+184x^2+13x+119$
• $y^2=66x^6+59x^5+158x^4+123x^3+112x^2+8x+57$
• $y^2=20x^6+162x^5+24x^4+168x^3+4x^2+152x+130$
• $y^2=170x^6+53x^5+167x^4+125x^3+168x^2+151x+103$
• $y^2=163x^6+143x^5+11x^4+149x^3+10x^2+10x+41$
• $y^2=88x^6+79x^5+30x^4+20x^3+86x^2+117x+22$
• $y^2=76x^6+145x^5+96x^4+8x^3+185x^2+74x+123$
• $y^2=81x^6+47x^5+185x^4+73x^3+36x^2+35x+21$
• $y^2=100x^6+184x^5+97x^4+177x^3+155x^2+28x+192$
• $y^2=102x^6+142x^5+2x^4+36x^3+20x^2+58x+29$
• $y^2=92x^6+125x^5+119x^4+177x^3+146x^2+150x+36$
• $y^2=58x^6+76x^5+119x^4+50x^3+52x^2+100x+117$
• $y^2=19x^6+132x^5+133x^4+127x^3+123x^2+80x+180$
• $y^2=89x^6+140x^5+99x^4+124x^3+172x^2+115x+160$
• $y^2=136x^6+39x^5+161x^4+89x^3+65x^2+129x+37$
• $y^2=14x^6+154x^5+6x^4+188x^3+87x^2+70x+150$
• $y^2=149x^6+15x^5+92x^4+88x^3+117x^2+125x+102$
• $y^2=92x^6+160x^5+151x^4+149x^3+121x^2+40x+33$
• $y^2=111x^6+90x^5+98x^4+14x^3+118x^2+12x+86$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 29055 1374040005 51676117079535 1925144786215617525 71708910713168138108400 2671084580066587565478077805 99495242843763620887184413567695 3706098377210444230491591851302361925 138048458689188174678055166902231833930855 5142167038129222371445837886030778930081926400

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 147 36887 7188165 1387503739 267785206002 51682532469959 9974730102163281 1925122949467230931 371548729883636735175 71708904873338269761182

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
 The endomorphism algebra of this simple isogeny class is 4.0.30262893.1.
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.bv_bjn $2$ (not in LMFDB)