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 is principally polarizable and contains the Jacobians of 49 curves (of which all are hyperelliptic):

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

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

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)