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

• Label: 2.157.abs_bes
• 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:	$( 1 - 22 x + 157 x^{2} )^{2}$
	$1 - 44 x + 798 x^{2} - 6908 x^{3} + 24649 x^{4}$
Frobenius angles:	$\pm0.158946998144$, $\pm0.158946998144$
Angle rank:	$1$ (numerical)
Jacobians:	$49$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$18496$	$599270400$	$14973866073664$	$369169982760960000$	$9099154080552453998656$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$114$	$24310$	$3869322$	$607613998$	$95389979874$	$14976087147430$	$2351243459480442$	$369145196171522398$	$57955795554615614034$	$9099059900933560926550$

Jacobians and polarizations

This isogeny class contains the Jacobians of 49 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=120x^6+130x^5+109x^4+32x^3+64x^2+109x+47$
• $y^2=5x^6+149x^3+80$
• $y^2=131x^6+95x^5+122x^4+145x^3+12x^2+131x+114$
• $y^2=116x^6+88x^4+88x^2+116$
• $y^2=5x^6+98x^3+87$
• $y^2=20x^6+134x^5+76x^4+x^3+108x^2+151x+34$
• $y^2=93x^6+99x^5+38x^4+21x^3+38x^2+99x+93$
• $y^2=151x^6+42x^5+17x^4+26x^3+17x^2+42x+151$
• $y^2=30x^6+20x^5+39x^4+3x^3+146x^2+98x+31$
• $y^2=45x^6+14x^5+141x^4+50x^3+75x^2+39x+128$
• $y^2=38x^6+30x^5+93x^4+146x^3+98x^2+4x+28$
• $y^2=72x^6+119x^4+119x^2+72$
• $y^2=18x^6+3x^5+57x^4+119x^3+39x^2+111x+26$
• $y^2=13x^6+135x^5+139x^4+55x^3+26x^2+80x+112$
• $y^2=66x^6+88x^5+139x^4+89x^3+55x^2+110x+45$
• $y^2=83x^6+89x^5+18x^4+61x^2+37x+50$
• $y^2=77x^6+127x^5+7x^4+102x^3+98x^2+86x+123$
• $y^2=30x^6+15x^4+15x^2+30$
• $y^2=5x^6+2x^3+38$
• $y^2=136x^6+3x^5+89x^4+22x^3+49x^2+13x+151$
• and

• $y^2=23x^6+82x^4+82x^2+23$
• $y^2=88x^6+59x^5+65x^4+5x^3+65x^2+59x+88$
• $y^2=92x^6+19x^4+19x^2+92$
• $y^2=88x^6+73x^5+153x^4+45x^3+48x^2+142x+153$
• $y^2=87x^6+51x^5+41x^4+53x^3+53x^2+38x+31$
• $y^2=5x^6+5x^3+73$
• $y^2=93x^6+14x^4+14x^2+93$
• $y^2=137x^6+61x^5+120x^4+80x^3+82x^2+41x+38$
• $y^2=5x^6+26x^3+119$
• $y^2=80x^6+15x^5+42x^4+28x^3+67x^2+8x+88$
• $y^2=43x^6+91x^5+52x^4+38x^3+138x^2+28x+102$
• $y^2=47x^6+123x^5+83x^4+107x^3+59x^2+7x+25$
• $y^2=5x^6+45x^3+34$
• $y^2=9x^6+111x^5+146x^4+120x^3+87x^2+62x+121$
• $y^2=110x^6+119x^5+45x^4+56x^3+55x^2+139x+105$
• $y^2=18x^6+108x^5+53x^4+36x^3+45x^2+37x+63$
• $y^2=12x^6+58x^5+151x^4+72x^3+151x^2+59x+45$
• $y^2=104x^6+124x^5+138x^4+28x^3+99x^2+130x+102$
• $y^2=74x^6+9x^5+147x^3+109x+15$
• $y^2=144x^6+93x^5+150x^4+80x^3+150x^2+93x+144$
• $y^2=124x^6+50x^5+11x^4+117x^3+14x^2+129x+124$
• $y^2=44x^6+70x^5+73x^4+69x^3+79x^2+94x+35$
• $y^2=63x^6+148x^5+144x^4+29x^3+40x^2+56x+83$
• $y^2=20x^6+13x^5+95x^4+125x^3+51x^2+35x+149$
• $y^2=60x^6+97x^5+144x^4+136x^3+107x^2+122x+11$
• $y^2=105x^6+64x^5+81x^4+74x^3+81x^2+64x+105$
• $y^2=46x^6+14x^5+110x^4+73x^3+93x^2+132x+111$
• $y^2=136x^6+63x^5+63x^4+35x^3+119x^2+155x+135$
• $y^2=40x^6+127x^5+16x^4+9x^3+130x^2+36x+81$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{157}$

The isogeny class factors as 1.157.aw^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-1}) \)$)$

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
2.157.a_ago	$2$	(not in LMFDB)
2.157.bs_bes	$2$	(not in LMFDB)
2.157.w_mp	$3$	(not in LMFDB)