Abelian variety isogeny class 2.199.abw_bkw over $\F_{199}$

• Label: 2.199.abw_bkw
• Base field: $\F_{199}$
• 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:	$\F_{199}$
Dimension:	$2$
L-polynomial:	$( 1 - 28 x + 199 x^{2} )( 1 - 20 x + 199 x^{2} )$
	$1 - 48 x + 958 x^{2} - 9552 x^{3} + 39601 x^{4}$
Frobenius angles:	$\pm0.0391815390403$, $\pm0.249200223051$
Angle rank:	$2$ (numerical)
Jacobians:	$90$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$30960$	$1552953600$	$62093622472560$	$2459388936883507200$	$97393642291828872658800$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$152$	$39214$	$7879304$	$1568248606$	$312079488632$	$62103829181902$	$12358663979948648$	$2459374186682549566$	$489415464067324730456$	$97393677359471287288174$

Jacobians and polarizations

This isogeny class contains the Jacobians of 90 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=54x^6+113x^5+2x^4+119x^3+131x^2+104x+116$
• $y^2=155x^6+183x^5+75x^4+11x^3+91x^2+165x+151$
• $y^2=120x^6+113x^5+152x^4+91x^3+122x^2+53x+55$
• $y^2=28x^6+81x^5+145x^4+43x^3+159x^2+60x+35$
• $y^2=140x^6+95x^5+196x^4+34x^3+140x^2+169x+32$
• $y^2=69x^6+119x^5+42x^4+181x^3+134x^2+11x+44$
• $y^2=141x^6+145x^5+20x^4+x^3+10x^2+86x+142$
• $y^2=10x^6+64x^5+44x^4+16x^3+75x^2+175x+137$
• $y^2=55x^6+142x^5+113x^4+49x^3+113x^2+142x+55$
• $y^2=157x^6+13x^5+62x^4+30x^3+14x^2+168x+37$
• $y^2=176x^6+43x^5+175x^4+13x^3+160x^2+11x+172$
• $y^2=144x^6+71x^5+49x^4+150x^3+31x^2+197x+106$
• $y^2=29x^6+114x^5+174x^4+127x^3+134x^2+102x+96$
• $y^2=150x^6+186x^5+141x^4+122x^3+191x^2+91x+84$
• $y^2=33x^6+129x^5+15x^4+112x^3+112x^2+114x+39$
• $y^2=135x^6+16x^5+10x^4+183x^3+72x^2+83x+174$
• $y^2=173x^6+5x^5+29x^4+18x^3+29x^2+5x+173$
• $y^2=161x^6+37x^5+106x^4+137x^3+98x^2+115x+3$
• $y^2=153x^6+23x^5+159x^4+175x^3+143x^2+61x+68$
• $y^2=65x^6+17x^5+187x^4+113x^3+83x^2+24x+8$
• and

• $y^2=31x^6+159x^5+144x^4+60x^3+198x^2+113x+168$
• $y^2=69x^6+90x^5+187x^3+90x+69$
• $y^2=127x^6+87x^5+29x^4+187x^3+54x^2+192x+173$
• $y^2=162x^6+77x^5+115x^4+113x^3+85x^2+111x+128$
• $y^2=51x^6+192x^5+157x^4+52x^3+157x^2+192x+51$
• $y^2=67x^6+62x^5+27x^4+57x^3+27x^2+62x+67$
• $y^2=149x^6+100x^5+94x^4+164x^3+123x^2+48x+47$
• $y^2=76x^6+151x^5+100x^4+71x^3+89x^2+91x+167$
• $y^2=120x^6+60x^5+87x^4+84x^3+87x^2+60x+120$
• $y^2=130x^6+106x^5+81x^4+198x^3+60x^2+181x+191$
• $y^2=67x^6+105x^5+125x^4+76x^3+105x^2+122x+195$
• $y^2=77x^6+12x^5+138x^4+84x^3+169x^2+45x+117$
• $y^2=194x^6+166x^5+26x^4+177x^3+33x^2+82x+166$
• $y^2=116x^6+11x^5+189x^4+24x^3+134x^2+17x+116$
• $y^2=153x^6+67x^5+67x^4+95x^3+75x^2+127x+128$
• $y^2=19x^6+152x^5+116x^4+175x^3+110x^2+128x+74$
• $y^2=124x^6+28x^5+136x^4+114x^3+175x^2+130x+58$
• $y^2=28x^6+46x^5+108x^4+105x^3+138x^2+174x+2$
• $y^2=113x^6+49x^5+165x^4+136x^3+56x^2+91x+42$
• $y^2=74x^6+179x^5+165x^4+184x^3+77x^2+90x+104$
• $y^2=193x^6+111x^5+9x^4+110x^3+112x^2+99x+17$
• $y^2=165x^6+184x^5+20x^4+154x^3+94x^2+164x+5$
• $y^2=84x^6+103x^5+29x^4+184x^3+29x^2+103x+84$
• $y^2=39x^6+57x^5+182x^4+93x^3+99x^2+21x+7$
• $y^2=24x^6+190x^5+45x^4+132x^3+176x^2+145x+83$
• $y^2=125x^6+69x^5+95x^4+139x^3+165x^2+9x+146$
• $y^2=152x^6+46x^5+140x^4+24x^3+144x^2+26x+195$
• $y^2=133x^6+9x^5+126x^4+38x^3+124x^2+57x+173$
• $y^2=10x^6+136x^5+7x^4+46x^3+95x^2+58x+61$
• $y^2=141x^6+181x^5+168x^4+136x^3+129x^2+119x+197$
• $y^2=154x^6+65x^5+64x^4+146x^3+148x^2+147x+20$
• $y^2=84x^6+91x^5+132x^4+89x^3+96x^2+25x+190$
• $y^2=133x^6+101x^5+169x^4+177x^3+60x^2+80x+42$
• $y^2=94x^6+143x^5+9x^4+31x^3+163x^2+85x+62$
• $y^2=76x^6+38x^5+195x^4+115x^3+35x^2+196x+71$
• $y^2=141x^6+154x^5+143x^4+11x^3+194x^2+155x+138$
• $y^2=92x^6+150x^5+17x^4+120x^3+72x^2+88x+195$
• $y^2=20x^6+21x^5+132x^4+148x^3+186x^2+99x+116$
• $y^2=105x^6+174x^5+26x^4+155x^3+26x^2+174x+105$
• $y^2=88x^6+15x^5+29x^4+117x^3+75x^2+133x+103$
• $y^2=103x^6+146x^5+11x^4+156x^3+189x^2+75x+39$
• $y^2=4x^6+187x^5+102x^4+63x^3+35x^2+25x+132$
• $y^2=173x^6+131x^5+190x^4+7x^3+193x^2+152x+121$
• $y^2=77x^6+193x^5+104x^4+148x^3+131x^2+45x+173$
• $y^2=137x^6+15x^5+85x^4+115x^3+85x^2+15x+137$
• $y^2=168x^6+7x^5+66x^4+158x^3+66x^2+7x+168$
• $y^2=120x^6+47x^5+172x^4+39x^3+196x^2+159x+37$
• $y^2=113x^6+173x^5+42x^4+84x^3+198x^2+159x+69$
• $y^2=28x^6+196x^5+66x^4+174x^3+148x^2+47x+163$
• $y^2=174x^6+154x^5+53x^4+102x^3+14x^2+97x+110$
• $y^2=124x^6+134x^5+54x^4+103x^3+106x^2+184x+140$
• $y^2=181x^6+141x^5+93x^4+12x^3+84x^2+63x+180$
• $y^2=198x^6+164x^5+195x^4+154x^3+12x^2+83x+27$
• $y^2=182x^6+76x^5+35x^4+73x^3+121x^2+119x+8$
• $y^2=158x^6+100x^5+70x^4+170x^3+10x^2+73x+142$
• $y^2=150x^6+64x^5+97x^4+87x^3+60x^2+39x+191$
• $y^2=52x^6+154x^5+98x^4+109x^3+167x^2+99x+176$
• $y^2=119x^6+176x^5+42x^4+160x^3+109x^2+32x+96$
• $y^2=129x^6+70x^5+100x^4+7x^3+83x^2+59x+9$
• $y^2=11x^6+147x^5+120x^4+46x^3+60x^2+89x+33$
• $y^2=131x^6+4x^5+125x^4+4x^3+12x^2+99x+150$
• $y^2=176x^6+77x^5+45x^4+40x^3+157x^2+160x+55$
• $y^2=48x^6+33x^5+125x^4+137x^3+125x^2+33x+48$
• $y^2=185x^6+122x^5+109x^4+3x^3+99x^2+72x+105$
• $y^2=53x^6+178x^5+150x^4+30x^3+52x^2+5x+80$
• $y^2=95x^6+182x^5+130x^4+77x^3+130x^2+182x+95$
• $y^2=98x^6+186x^5+63x^4+126x^3+63x^2+186x+98$
• $y^2=47x^6+120x^5+183x^4+78x^3+150x^2+158x+192$
• $y^2=127x^6+128x^5+142x^4+84x^3+183x^2+100x+68$
• $y^2=175x^6+93x^5+32x^4+187x^3+43x^2+186x+35$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{199}$.

Endomorphism algebra over $\F_{199}$

The isogeny class factors as 1.199.abc $\times$ 1.199.au and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.199.abc : \(\Q(\sqrt{-3}) \).
• 1.199.au : \(\Q(\sqrt{-11}) \).

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
2.199.ai_agg	$2$	(not in LMFDB)
2.199.i_agg	$2$	(not in LMFDB)
2.199.bw_bkw	$2$	(not in LMFDB)
2.199.aj_gw	$3$	(not in LMFDB)
2.199.ad_cg	$3$	(not in LMFDB)