Abelian variety isogeny class 2.193.abw_bkw over $\F_{193}$

• Label: 2.193.abw_bkw
• Base field: $\F_{193}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{193}$
Dimension:	$2$
L-polynomial:	$( 1 - 26 x + 193 x^{2} )( 1 - 22 x + 193 x^{2} )$
	$1 - 48 x + 958 x^{2} - 9264 x^{3} + 37249 x^{4}$
Frobenius angles:	$\pm0.114714697559$, $\pm0.209145594264$
Angle rank:	$2$ (numerical)
Jacobians:	$132$

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28896$	$1373137920$	$51679443983328$	$1925199672057446400$	$71709242656146423177696$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$146$	$36862$	$7188626$	$1387543294$	$267786445586$	$51682558576894$	$9974730511235090$	$1925122954165498366$	$371548729915767574418$	$71708904873244677840382$

Jacobians and polarizations

This isogeny class contains the Jacobians of 132 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=29x^6+80x^5+163x^4+90x^3+83x^2+178x+89$
• $y^2=73x^6+24x^5+16x^4+135x^3+16x^2+24x+73$
• $y^2=75x^6+120x^5+183x^4+125x^3+60x^2+96x+123$
• $y^2=79x^6+128x^5+111x^4+163x^3+111x^2+128x+79$
• $y^2=39x^6+82x^5+124x^4+8x^3+124x^2+82x+39$
• $y^2=95x^6+16x^5+187x^4+30x^3+112x^2+21x+85$
• $y^2=182x^6+31x^5+161x^4+131x^3+23x^2+17x+91$
• $y^2=154x^6+161x^5+128x^4+112x^3+128x^2+161x+154$
• $y^2=71x^6+4x^5+97x^4+190x^3+97x^2+4x+71$
• $y^2=175x^6+47x^5+185x^4+59x^3+184x^2+111x+44$
• $y^2=106x^6+19x^5+176x^4+123x^3+10x^2+147x+184$
• $y^2=52x^6+150x^5+172x^4+12x^3+172x^2+150x+52$
• $y^2=174x^6+29x^5+107x^4+14x^3+73x^2+101x+39$
• $y^2=73x^6+87x^5+7x^4+162x^3+188x^2+167x+6$
• $y^2=64x^6+157x^5+110x^4+177x^3+177x^2+191x+86$
• $y^2=120x^6+145x^5+168x^4+75x^3+187x^2+189x+41$
• $y^2=45x^6+118x^5+62x^4+154x^3+62x^2+118x+45$
• $y^2=65x^6+76x^5+186x^4+192x^2+171x+17$
• $y^2=159x^6+99x^5+82x^4+127x^3+82x^2+99x+159$
• $y^2=11x^6+164x^5+115x^4+140x^3+115x^2+164x+11$
• and

• $y^2=45x^6+111x^5+31x^4+114x^3+31x^2+111x+45$
• $y^2=181x^6+12x^5+156x^4+97x^3+133x^2+84x+62$
• $y^2=90x^5+40x^4+119x^3+40x^2+90x$
• $y^2=19x^6+173x^5+20x^4+111x^3+183x^2+102x+129$
• $y^2=174x^6+45x^5+83x^4+74x^3+83x^2+45x+174$
• $y^2=156x^6+125x^5+50x^4+81x^3+58x^2+94x+57$
• $y^2=22x^6+181x^5+30x^4+5x^3+30x^2+181x+22$
• $y^2=17x^6+81x^5+166x^4+87x^3+108x^2+56x+136$
• $y^2=132x^6+48x^5+100x^4+49x^3+100x^2+48x+132$
• $y^2=92x^6+81x^5+86x^4+160x^3+87x^2+17x+156$
• $y^2=16x^5+52x^4+65x^3+53x^2+51x+181$
• $y^2=108x^6+106x^4+106x^3+140x^2+108x+53$
• $y^2=153x^6+22x^5+130x^4+109x^3+130x^2+22x+153$
• $y^2=14x^6+121x^5+43x^4+49x^3+43x^2+121x+14$
• $y^2=154x^6+187x^5+91x^4+2x^3+61x^2+18x+106$
• $y^2=146x^6+59x^5+90x^4+24x^3+90x^2+59x+146$
• $y^2=105x^6+152x^5+158x^4+41x^3+158x^2+152x+105$
• $y^2=185x^6+66x^5+105x^4+144x^3+176x^2+71x+64$
• $y^2=79x^6+184x^5+19x^4+99x^3+183x^2+70x+4$
• $y^2=10x^6+100x^5+164x^4+189x^3+119x^2+28x+120$
• $y^2=82x^6+50x^5+49x^4+16x^3+185x^2+149x+100$
• $y^2=190x^6+46x^5+46x^4+11x^3+46x^2+46x+190$
• $y^2=16x^6+128x^5+129x^4+16x^3+129x^2+128x+16$
• $y^2=77x^6+100x^5+151x^4+65x^3+151x^2+100x+77$
• $y^2=30x^6+114x^5+62x^4+139x^3+62x^2+114x+30$
• $y^2=53x^6+149x^5+89x^4+192x^3+166x^2+131x+184$
• $y^2=178x^6+119x^5+69x^4+75x^3+69x^2+119x+178$
• $y^2=147x^6+95x^5+183x^4+132x^3+183x^2+95x+147$
• $y^2=25x^6+60x^5+154x^4+179x^3+154x^2+60x+25$
• $y^2=121x^6+49x^5+133x^4+123x^3+133x^2+49x+121$
• $y^2=85x^6+109x^5+60x^4+36x^3+60x^2+109x+85$
• $y^2=104x^6+117x^5+172x^4+134x^3+67x^2+30x+65$
• $y^2=21x^6+107x^5+69x^4+169x^3+69x^2+107x+21$
• $y^2=178x^6+22x^5+57x^4+73x^3+60x^2+40x+25$
• $y^2=174x^6+109x^5+105x^4+101x^3+180x^2+14x+146$
• $y^2=148x^6+98x^5+68x^4+155x^3+156x^2+115x+167$
• $y^2=19x^6+189x^5+119x^4+75x^3+156x^2+192x+123$
• $y^2=127x^6+16x^5+149x^4+141x^3+49x^2+94x+51$
• $y^2=8x^6+191x^5+156x^4+27x^3+7x^2+180x+15$
• $y^2=99x^6+121x^5+48x^4+158x^3+144x^2+124x+164$
• $y^2=168x^6+130x^5+175x^4+115x^3+139x^2+12x+97$
• $y^2=162x^6+9x^5+80x^4+135x^3+80x^2+9x+162$
• $y^2=70x^6+122x^5+57x^4+125x^3+84x^2+185x+143$
• $y^2=17x^6+116x^5+126x^4+2x^3+126x^2+116x+17$
• $y^2=20x^6+121x^5+2x^4+75x^3+64x^2+191x+125$
• $y^2=83x^6+168x^5+9x^4+166x^3+69x^2+96x+189$
• $y^2=51x^6+121x^5+23x^4+75x^3+23x^2+121x+51$
• $y^2=111x^6+56x^5+67x^4+9x^3+67x^2+56x+111$
• $y^2=17x^6+105x^5+70x^4+75x^3+176x^2+173x+120$
• $y^2=48x^6+31x^5+53x^4+48x^3+53x^2+31x+48$
• $y^2=39x^6+62x^5+55x^4+29x^3+59x^2+79x+97$
• $y^2=68x^6+29x^5+70x^4+109x^3+70x^2+29x+68$
• $y^2=61x^6+22x^5+182x^4+5x^3+41x^2+60x+61$
• $y^2=5x^6+72x^5+75x^4+123x^3+186x^2+161x+15$
• $y^2=133x^6+82x^5+93x^4+45x^3+93x^2+82x+133$
• $y^2=153x^6+21x^5+167x^4+34x^3+167x^2+21x+153$
• $y^2=126x^6+185x^5+32x^4+110x^3+32x^2+185x+126$
• $y^2=24x^6+7x^5+47x^4+165x^3+47x^2+7x+24$
• $y^2=158x^6+159x^5+179x^4+34x^3+179x^2+159x+158$
• $y^2=113x^6+35x^5+48x^4+93x^3+77x^2+31x+155$
• $y^2=136x^6+158x^5+185x^4+111x^3+155x^2+70x+172$
• $y^2=4x^6+11x^5+162x^4+97x^3+101x^2+52x+10$
• $y^2=119x^6+8x^5+103x^4+30x^3+103x^2+8x+119$
• $y^2=155x^6+20x^5+51x^4+132x^3+174x^2+68x+98$
• $y^2=70x^6+99x^5+82x^4+51x^3+35x^2+116x+73$
• $y^2=42x^6+45x^5+130x^4+55x^3+144x^2+186x+132$
• $y^2=120x^6+35x^5+135x^4+139x^3+158x^2+162x+38$
• $y^2=90x^5+180x^4+32x^3+180x^2+90x$
• $y^2=76x^6+136x^5+29x^4+94x^3+190x^2+89x+130$
• $y^2=58x^6+64x^5+167x^4+117x^3+133x^2+6x+82$
• $y^2=31x^6+156x^5+127x^4+186x^3+127x^2+156x+31$
• $y^2=79x^6+168x^5+160x^4+80x^3+160x^2+168x+79$
• $y^2=163x^6+121x^5+178x^4+69x^3+47x^2+96x+132$
• $y^2=10x^6+115x^5+30x^4+66x^3+30x^2+115x+10$
• $y^2=27x^6+105x^5+127x^4+69x^3+127x^2+105x+27$
• $y^2=133x^6+10x^5+119x^4+61x^3+119x^2+10x+133$
• $y^2=58x^6+42x^5+82x^4+5x^3+82x^2+42x+58$
• $y^2=182x^6+21x^5+100x^4+162x^3+100x^2+21x+182$
• $y^2=97x^6+29x^5+13x^4+130x^3+83x^2+115x+97$
• $y^2=140x^6+129x^5+62x^4+191x^3+152x^2+17x+51$
• $y^2=124x^6+98x^5+114x^4+80x^3+114x^2+98x+124$
• $y^2=106x^6+188x^5+192x^4+28x^3+97x^2+47x+35$
• $y^2=41x^6+63x^5+10x^4+181x^3+159x^2+66x+189$
• $y^2=85x^6+46x^5+48x^4+190x^3+143x^2+131x+12$
• $y^2=109x^6+144x^5+143x^4+182x^3+170x^2+28x+107$
• $y^2=78x^6+97x^5+170x^4+81x^3+155x^2+58x+146$
• $y^2=170x^6+126x^5+19x^4+167x^3+19x^2+126x+170$
• $y^2=31x^6+167x^5+104x^4+180x^3+104x^2+167x+31$
• $y^2=107x^6+98x^5+68x^4+125x^3+140x^2+185x+55$
• $y^2=47x^6+54x^5+25x^4+186x^3+92x^2+93x+80$
• $y^2=111x^6+165x^5+x^4+43x^3+x^2+165x+111$
• $y^2=91x^6+173x^5+99x^4+176x^3+82x^2+22x+183$
• $y^2=82x^6+169x^5+94x^4+12x^3+94x^2+169x+82$
• $y^2=173x^6+14x^5+113x^4+12x^3+135x^2+162x+39$
• $y^2=73x^6+42x^5+20x^4+104x^3+157x^2+35x+107$
• $y^2=120x^6+74x^5+53x^4+121x^3+111x^2+94x+17$
• $y^2=156x^6+102x^5+187x^4+43x^3+135x^2+167x+105$
• $y^2=102x^6+50x^5+156x^4+36x^3+156x^2+50x+102$
• $y^2=61x^6+82x^5+126x^4+62x^3+66x^2+32x+82$
• $y^2=125x^6+155x^5+138x^4+187x^3+4x^2+148x+79$
• $y^2=9x^6+67x^5+142x^4+117x^3+120x^2+23x+192$
• $y^2=30x^6+80x^5+80x^4+113x^3+80x^2+80x+30$
• $y^2=175x^6+153x^5+176x^4+8x^3+176x^2+153x+175$
• $y^2=151x^6+26x^5+90x^4+22x^3+155x^2+176x+124$
• $y^2=180x^6+157x^5+18x^4+182x^3+18x^2+157x+180$
• $y^2=183x^6+90x^5+85x^4+110x^3+85x^2+90x+183$
• $y^2=40x^6+21x^5+14x^4+67x^3+127x^2+71x+77$
• $y^2=111x^6+81x^5+123x^4+130x^3+123x^2+81x+111$
• $y^2=37x^6+55x^5+95x^4+87x^3+81x^2+34x+99$
• $y^2=171x^6+144x^5+45x^4+186x^3+58x^2+86x+30$
• $y^2=73x^6+182x^5+46x^4+22x^3+60x^2+83x+94$
• $y^2=48x^6+100x^5+10x^4+127x^3+10x^2+100x+48$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{193}$.

Endomorphism algebra over $\F_{193}$

The isogeny class factors as 1.193.aba $\times$ 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:

• 1.193.aba : \(\Q(\sqrt{-6}) \).
• 1.193.aw : \(\Q(\sqrt{-2}) \).

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.ae_ahe	$2$	(not in LMFDB)
2.193.e_ahe	$2$	(not in LMFDB)
2.193.bw_bkw	$2$	(not in LMFDB)