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

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

Invariants

Base field:	$\F_{193}$
Dimension:	$2$
L-polynomial:	$1 - 48 x + 957 x^{2} - 9264 x^{3} + 37249 x^{4}$
Frobenius angles:	$\pm0.106782388193$, $\pm0.213534342372$
Angle rank:	$2$ (numerical)
Number field:	4.0.624025.2
Galois group:	$D_{4}$
Jacobians:	$72$

This isogeny class is simple and geometrically 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28895$	$1373061505$	$51678407454320$	$1925192198540640025$	$71709205251780376622375$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$146$	$36860$	$7188482$	$1387537908$	$267786305906$	$51682555822430$	$9974730469423922$	$1925122953719239588$	$371548729914231256706$	$71708904873314513132300$

Jacobians and polarizations

This isogeny class contains the Jacobians of 72 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=9x^6+78x^5+141x^4+79x^3+190x^2+124x+61$
• $y^2=99x^6+118x^5+145x^4+22x^3+56x^2+97x+184$
• $y^2=180x^6+143x^5+150x^4+117x^3+9x^2+85x+9$
• $y^2=80x^6+179x^5+55x^4+160x^3+54x^2+79x+33$
• $y^2=125x^6+108x^5+151x^4+84x^3+23x^2+182x+95$
• $y^2=134x^6+74x^5+183x^4+54x^3+169x^2+12x+78$
• $y^2=141x^6+39x^5+12x^4+114x^3+42x^2+176x+7$
• $y^2=105x^6+62x^5+167x^4+178x^3+112x^2+132x+154$
• $y^2=3x^6+13x^5+42x^4+175x^3+8x^2+129x+32$
• $y^2=111x^6+160x^5+124x^4+161x^3+109x^2+93x+89$
• $y^2=8x^6+127x^5+50x^4+11x^3+100x^2+170x+103$
• $y^2=132x^6+166x^5+57x^4+48x^3+125x^2+26x+30$
• $y^2=15x^6+92x^5+85x^4+180x^3+59x^2+87x+152$
• $y^2=76x^6+166x^5+111x^4+16x^3+36x^2+148x+168$
• $y^2=68x^6+189x^4+47x^3+29x^2+114x+150$
• $y^2=154x^6+132x^5+120x^4+92x^3+186x^2+186x+111$
• $y^2=6x^6+26x^5+131x^4+158x^3+163x^2+171x+168$
• $y^2=101x^6+69x^5+123x^4+158x^3+111x^2+146x+126$
• $y^2=94x^6+79x^5+59x^4+50x^3+105x^2+110x+187$
• $y^2=132x^6+161x^5+169x^4+90x^3+171x^2+x+114$
• and

• $y^2=155x^6+160x^5+50x^4+168x^3+132x^2+16x+120$
• $y^2=8x^6+175x^5+45x^4+52x^3+28x^2+31x+119$
• $y^2=148x^6+147x^5+101x^4+149x^3+147x^2+181x+109$
• $y^2=112x^6+158x^5+79x^4+106x^3+46x^2+169x+22$
• $y^2=136x^6+123x^5+9x^4+97x^3+51x^2+26x+60$
• $y^2=124x^6+56x^5+15x^4+5x^3+55x^2+135x+165$
• $y^2=129x^6+65x^5+71x^4+149x^3+192x^2+54x+129$
• $y^2=160x^6+185x^5+92x^4+88x^3+76x^2+35x+114$
• $y^2=180x^6+181x^5+4x^4+27x^3+167x^2+5x+78$
• $y^2=186x^6+51x^5+145x^4+97x^3+33x^2+27x+153$
• $y^2=183x^6+163x^5+134x^4+76x^3+180x^2+73x+175$
• $y^2=125x^6+147x^5+84x^4+63x^3+94x^2+85x+46$
• $y^2=173x^6+57x^5+31x^4+128x^3+148x^2+62x+41$
• $y^2=105x^6+80x^5+171x^4+14x^3+9x^2+x+180$
• $y^2=155x^6+111x^5+82x^4+163x^3+181x^2+137x+80$
• $y^2=7x^6+163x^5+21x^4+42x^3+104x^2+164x+122$
• $y^2=139x^6+127x^5+184x^4+127x^3+43x^2+166x+24$
• $y^2=160x^6+127x^5+15x^4+136x^3+170x^2+70x+164$
• $y^2=144x^6+71x^5+127x^4+181x^3+118x^2+183x+56$
• $y^2=76x^6+102x^5+145x^4+94x^3+166x^2+93x+120$
• $y^2=64x^6+118x^5+133x^4+134x^3+127x^2+42x+159$
• $y^2=81x^6+104x^5+47x^4+88x^3+148x^2+109x+73$
• $y^2=69x^6+62x^5+47x^4+179x^3+32x^2+45x+178$
• $y^2=149x^6+129x^5+46x^4+7x^3+49x^2+142x+125$
• $y^2=103x^6+97x^5+139x^4+106x^3+92x^2+20x+15$
• $y^2=176x^6+111x^5+166x^4+58x^3+133x^2+43x+94$
• $y^2=31x^6+3x^5+80x^4+155x^3+96x^2+104x+70$
• $y^2=144x^6+132x^5+11x^4+134x^3+189x^2+186x+47$
• $y^2=166x^6+97x^5+191x^4+123x^3+135x^2+163x+178$
• $y^2=160x^6+187x^5+35x^4+130x^3+x^2+9x+165$
• $y^2=141x^6+105x^5+175x^4+82x^3+190x^2+185x+174$
• $y^2=119x^6+182x^5+181x^4+177x^3+156x^2+111x+29$
• $y^2=10x^6+139x^5+62x^4+124x^3+53x^2+180x+167$
• $y^2=65x^6+83x^5+145x^4+113x^3+76x^2+165x+113$
• $y^2=178x^6+14x^5+87x^4+178x^3+124x^2+31x+109$
• $y^2=171x^6+20x^5+2x^4+132x^3+100x^2+39x+15$
• $y^2=90x^6+179x^5+136x^4+154x^3+186x^2+138x+125$
• $y^2=159x^6+28x^5+98x^4+161x^3+107x^2+35x+63$
• $y^2=13x^6+43x^5+110x^4+12x^3+4x^2+46x+137$
• $y^2=117x^6+172x^5+120x^4+177x^3+108x^2+46x+52$
• $y^2=122x^6+181x^5+47x^4+25x^3+168x^2+39x+57$
• $y^2=26x^6+121x^5+11x^4+175x^3+145x^2+73x+126$
• $y^2=31x^6+173x^5+55x^4+109x^3+34x^2+177x+171$
• $y^2=74x^6+175x^5+128x^4+10x^3+100x^2+15x+178$
• $y^2=100x^6+139x^5+141x^4+82x^3+149x^2+165x+126$
• $y^2=185x^6+104x^5+61x^4+90x^3+100x^2+30x+114$
• $y^2=56x^6+174x^5+135x^4+90x^3+32x^2+38x+3$
• $y^2=124x^6+131x^5+157x^4+113x^3+44x^2+144x+6$
• $y^2=117x^6+145x^5+130x^4+167x^3+47x^2+63x+90$
• $y^2=102x^6+137x^5+173x^4+180x^3+58x^2+7x+48$
• $y^2=169x^6+183x^5+144x^4+148x^3+74x^2+129x+123$
• $y^2=51x^6+171x^5+111x^4+26x^3+17x+61$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{193}$

The endomorphism algebra of this simple isogeny class is 4.0.624025.2.

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.bw_bkv	$2$	(not in LMFDB)