Abelian variety isogeny class 2.157.abq_bcs over $\F_{157}$

• Label: 2.157.abq_bcs
• Base field: $\F_{157}$
• 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:	$\F_{157}$
Dimension:	$2$
L-polynomial:	$( 1 - 24 x + 157 x^{2} )( 1 - 18 x + 157 x^{2} )$
	$1 - 42 x + 746 x^{2} - 6594 x^{3} + 24649 x^{4}$
Frobenius angles:	$\pm0.0929086555916$, $\pm0.244930514047$
Angle rank:	$2$ (numerical)
Jacobians:	$112$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$18760$	$600920320$	$14976560509960$	$369163332111974400$	$9099098197779851753800$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$116$	$24378$	$3870020$	$607603054$	$95389394036$	$14976073959306$	$2351243261143172$	$369145194208968286$	$57955795549081319540$	$9099059901195209123418$

Jacobians and polarizations

This isogeny class contains the Jacobians of 112 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=109x^6+150x^5+58x^4+48x^3+62x^2+105x+34$
• $y^2=85x^6+78x^5+45x^4+116x^3+133x^2+110x+26$
• $y^2=83x^6+112x^5+73x^4+12x^3+73x^2+112x+83$
• $y^2=61x^6+82x^5+59x^4+25x^3+113x^2+88x+72$
• $y^2=62x^6+13x^5+109x^4+121x^3+141x^2+79x+8$
• $y^2=20x^6+64x^5+91x^4+112x^3+5x^2+152x+144$
• $y^2=138x^6+112x^5+125x^4+56x^3+125x^2+112x+138$
• $y^2=95x^6+103x^5+107x^4+123x^3+154x^2+91$
• $y^2=92x^6+35x^5+62x^4+12x^3+156x^2+82x+31$
• $y^2=105x^6+12x^5+15x^4+63x^3+54x^2+152x+15$
• $y^2=96x^6+145x^5+145x^4+130x^3+72x^2+77x+13$
• $y^2=43x^6+80x^5+73x^4+20x^3+125x^2+28x+50$
• $y^2=139x^6+17x^5+50x^4+98x^3+132x^2+45x+48$
• $y^2=55x^6+46x^5+130x^4+20x^3+127x^2+113x+72$
• $y^2=59x^6+37x^5+6x^4+125x^3+148x^2+115x+19$
• $y^2=25x^6+46x^5+43x^4+131x^3+71x^2+100x+154$
• $y^2=14x^6+90x^5+28x^4+49x^3+22x^2+103x+139$
• $y^2=33x^6+89x^5+31x^4+14x^3+106x^2+138x+142$
• $y^2=62x^6+130x^5+140x^4+75x^3+64x^2+147x+62$
• $y^2=79x^6+50x^5+142x^4+18x^3+135x^2+154x+115$
• and

• $y^2=135x^6+117x^5+23x^4+99x^3+23x^2+117x+135$
• $y^2=87x^6+83x^4+41x^3+31x^2+42x+136$
• $y^2=72x^6+63x^5+59x^4+69x^3+26x^2+98x+18$
• $y^2=37x^6+89x^5+45x^4+30x^3+20x^2+103x+104$
• $y^2=41x^6+84x^5+37x^4+82x^3+42x^2+101x+90$
• $y^2=4x^6+111x^5+51x^4+59x^3+133x^2+52x+5$
• $y^2=70x^6+5x^5+149x^4+87x^3+83x^2+60x+15$
• $y^2=84x^6+97x^5+112x^4+124x^3+59x^2+117x+18$
• $y^2=111x^6+17x^5+56x^4+135x^3+32x^2+25$
• $y^2=112x^6+130x^5+103x^4+39x^3+90x^2+49x+8$
• $y^2=30x^6+4x^5+11x^4+71x^3+84x^2+78x+63$
• $y^2=63x^6+62x^5+116x^4+75x^3+109x^2+126x+41$
• $y^2=116x^6+139x^5+86x^4+70x^3+81x^2+155x+45$
• $y^2=70x^6+95x^5+7x^4+148x^3+148x^2+11x+84$
• $y^2=98x^6+31x^5+115x^4+118x^3+24x^2+94x+56$
• $y^2=133x^6+34x^5+28x^4+45x^3+33x^2+94x+70$
• $y^2=115x^6+59x^5+45x^4+123x^3+45x^2+59x+115$
• $y^2=147x^6+22x^5+127x^4+40x^3+127x^2+22x+147$
• $y^2=70x^6+22x^5+65x^4+5x^3+98x^2+19x+153$
• $y^2=43x^6+15x^5+148x^4+152x^3+52x^2+53x+63$
• $y^2=61x^6+81x^5+49x^4+119x^3+101x^2+4x+53$
• $y^2=20x^6+2x^5+63x^4+40x^3+131x^2+111x+98$
• $y^2=106x^6+112x^5+72x^4+20x^3+82x^2+25x+77$
• $y^2=66x^6+49x^5+67x^4+31x^3+33x^2+42x+60$
• $y^2=95x^6+62x^5+17x^4+58x^3+46x^2+39x+117$
• $y^2=27x^6+109x^5+129x^4+73x^3+73x^2+143x+119$
• $y^2=141x^6+76x^5+8x^4+4x^3+141x^2+156x+114$
• $y^2=39x^6+7x^5+132x^4+89x^3+36x^2+116x+58$
• $y^2=95x^6+31x^5+31x^4+96x^3+138x^2+93x+75$
• $y^2=9x^6+83x^5+107x^4+58x^3+29x^2+96x+84$
• $y^2=83x^6+143x^5+66x^4+24x^3+66x^2+143x+83$
• $y^2=69x^6+126x^5+11x^4+85x^3+151x^2+148x+46$
• $y^2=52x^6+10x^5+150x^4+63x^3+150x^2+10x+52$
• $y^2=136x^6+9x^5+6x^4+35x^3+68x^2+70x+82$
• $y^2=85x^6+104x^5+59x^4+12x^3+118x^2+16x+142$
• $y^2=103x^6+90x^5+116x^4+109x^3+116x^2+90x+103$
• $y^2=18x^6+128x^5+130x^4+14x^3+53x^2+44x+11$
• $y^2=33x^6+14x^5+56x^4+78x^3+132x^2+42x+9$
• $y^2=116x^6+46x^5+60x^4+24x^3+6x^2+134x+68$
• $y^2=141x^6+42x^5+88x^4+154x^3+130x^2+143x+66$
• $y^2=142x^6+71x^5+26x^4+149x^3+26x^2+71x+142$
• $y^2=32x^6+154x^5+70x^4+151x^3+103x^2+107x+120$
• $y^2=23x^6+15x^5+46x^4+61x^3+45x^2+20x+1$
• $y^2=85x^6+116x^5+8x^4+7x^3+83x^2+150x$
• $y^2=79x^6+86x^5+88x^4+39x^3+133x^2+57x+116$
• $y^2=87x^6+6x^5+87x^4+50x^3+80x^2+60x+9$
• $y^2=77x^6+26x^5+13x^4+104x^3+117x^2+90x+12$
• $y^2=152x^6+135x^5+6x^4+41x^3+52x^2+67x+4$
• $y^2=142x^6+74x^5+74x^4+46x^3+101x^2+57x+82$
• $y^2=126x^6+120x^5+70x^4+50x^3+125x^2+156x+77$
• $y^2=114x^6+45x^5+134x^4+105x^3+8x^2+79x+52$
• $y^2=114x^6+143x^5+42x^4+132x^3+50x^2+48x+34$
• $y^2=65x^6+5x^5+55x^4+154x^3+41x^2+114x+110$
• $y^2=152x^6+37x^5+97x^4+116x^3+9x^2+101x+7$
• $y^2=87x^6+68x^5+40x^4+54x^3+137x^2+48x+84$
• $y^2=23x^6+137x^5+137x^4+64x^3+41x^2+57x+25$
• $y^2=70x^6+143x^5+155x^4+87x^3+155x^2+16x+69$
• $y^2=154x^6+149x^5+126x^4+147x^3+49x^2+29x+70$
• $y^2=150x^6+41x^5+80x^4+19x^3+80x^2+41x+150$
• $y^2=6x^6+134x^5+38x^4+49x^3+43x^2+45x+86$
• $y^2=83x^6+144x^5+129x^4+109x^3+91x^2+38x+111$
• $y^2=112x^6+140x^5+106x^4+62x^3+49x^2+83x+78$
• $y^2=124x^6+55x^5+61x^4+116x^3+99x^2+123x+105$
• $y^2=152x^6+4x^5+75x^4+91x^3+37x^2+152x+63$
• $y^2=83x^6+16x^5+96x^4+5x^3+33x^2+135x+28$
• $y^2=59x^6+111x^5+39x^4+147x^3+102x^2+108x+112$
• $y^2=21x^6+51x^5+80x^4+68x^3+80x^2+51x+21$
• $y^2=147x^6+72x^5+156x^4+138x^3+105x^2+10x+87$
• $y^2=83x^6+14x^5+141x^4+14x^3+119x^2+105x+110$
• $y^2=112x^6+122x^5+130x^4+13x^3+57x^2+127x+59$
• $y^2=152x^6+67x^5+15x^4+72x^3+75x^2+61x+59$
• $y^2=77x^6+99x^5+122x^4+34x^3+148x^2+30x+6$
• $y^2=152x^6+148x^5+97x^4+55x^3+38x^2+111x+22$
• $y^2=38x^6+x^5+64x^4+145x^3+9x^2+80x+55$
• $y^2=4x^6+64x^5+152x^4+105x^3+130x^2+61x+109$
• $y^2=45x^6+55x^5+136x^4+97x^3+97x^2+96x+123$
• $y^2=103x^6+100x^5+24x^4+3x^3+71x^2+110x+38$
• $y^2=100x^6+3x^5+86x^4+70x^3+41x^2+76x+57$
• $y^2=74x^6+104x^5+34x^4+35x^3+18x^2+68x+140$
• $y^2=64x^6+104x^5+54x^4+77x^3+4x^2+149x+69$
• $y^2=16x^6+104x^5+11x^4+115x^3+44x^2+7x+114$
• $y^2=85x^6+101x^5+110x^4+84x^3+12x^2+109x+63$
• $y^2=87x^6+126x^5+8x^4+60x^3+90x^2+38x+8$
• $y^2=152x^6+31x^5+28x^4+129x^3+28x^2+31x+152$
• $y^2=86x^6+154x^5+104x^4+18x^3+127x^2+5x+77$
• $y^2=129x^6+17x^5+151x^4+103x^3+70x^2+81x+125$
• $y^2=85x^6+103x^5+66x^4+20x^3+73x^2+101x+146$
• $y^2=68x^6+129x^5+154x^4+29x^3+151x^2+144x+133$
• $y^2=74x^6+20x^5+118x^4+150x^3+91x^2+128x+87$
• $y^2=120x^6+59x^5+104x^4+73x^3+105x^2+119x+77$
• $y^2=72x^6+12x^5+67x^4+129x^3+141x^2+24x+109$
• $y^2=85x^6+27x^5+49x^4+139x^3+149x^2+131x+127$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{157}$.

Endomorphism algebra over $\F_{157}$

The isogeny class factors as 1.157.ay $\times$ 1.157.as and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.157.ay : \(\Q(\sqrt{-13}) \).
• 1.157.as : \(\Q(\sqrt{-19}) \).

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
2.157.ag_aeo	$2$	(not in LMFDB)
2.157.g_aeo	$2$	(not in LMFDB)
2.157.bq_bcs	$2$	(not in LMFDB)