Abelian variety isogeny class 2.149.abp_bbg over $\F_{149}$

• Label: 2.149.abp_bbg
• Base field: $\F_{149}$
• 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:	$\F_{149}$
Dimension:	$2$
L-polynomial:	$1 - 41 x + 708 x^{2} - 6109 x^{3} + 22201 x^{4}$
Frobenius angles:	$\pm0.0770400434079$, $\pm0.249339903978$
Angle rank:	$2$ (numerical)
Number field:	4.0.4269740.2
Galois group:	$D_{4}$
Jacobians:	$36$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$16760$	$487045600$	$10941983745920$	$242944511277296000$	$5393415051852451427800$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$109$	$21937$	$3307786$	$492903633$	$73439971689$	$10942525885942$	$1630436415074821$	$242935032115762113$	$36197319877822523554$	$5393400662170660894377$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 36 curves (of which all are hyperelliptic):

• $y^2=75 x^6+82 x^5+4 x^4+101 x^3+12 x^2+48 x+50$
• $y^2=50 x^6+126 x^5+42 x^4+59 x^3+52 x^2+134 x+34$
• $y^2=31 x^6+64 x^5+95 x^4+65 x^3+14 x^2+18 x+108$
• $y^2=35 x^6+47 x^5+113 x^4+45 x^3+50 x^2+17 x+147$
• $y^2=90 x^6+126 x^5+39 x^4+66 x^3+123 x^2+79 x+11$
• $y^2=86 x^6+x^5+66 x^4+45 x^3+24 x^2+113 x+71$
• $y^2=6 x^6+56 x^5+74 x^4+60 x^3+18 x^2+9 x+126$
• $y^2=136 x^6+120 x^5+90 x^4+96 x^3+143 x^2+78 x+74$
• $y^2=115 x^6+52 x^5+147 x^4+114 x^3+127 x^2+124 x+36$
• $y^2=122 x^6+140 x^5+120 x^4+76 x^3+130 x^2+116 x+66$
• $y^2=55 x^6+143 x^5+112 x^4+34 x^3+46 x^2+31 x+34$
• $y^2=146 x^6+28 x^5+62 x^4+74 x^3+142 x^2+92 x+8$
• $y^2=97 x^6+148 x^5+55 x^4+103 x^3+146 x^2+35 x$
• $y^2=141 x^6+127 x^5+115 x^4+8 x^3+5 x^2+34 x+7$
• $y^2=93 x^6+141 x^5+35 x^4+98 x^3+140 x^2+95 x+126$
• $y^2=10 x^6+124 x^5+84 x^4+12 x^3+82 x^2+93 x+12$
• $y^2=74 x^6+12 x^5+124 x^4+9 x^3+51 x^2+77 x+57$
• $y^2=72 x^6+141 x^5+128 x^4+146 x^3+128 x^2+122 x+65$
• $y^2=23 x^6+121 x^5+71 x^4+147 x^3+106 x^2+49 x+116$
• $y^2=76 x^6+22 x^5+58 x^4+95 x^3+5 x^2+8 x+64$
• and

• $y^2=111 x^6+11 x^5+110 x^4+86 x^3+77 x^2+35 x+83$
• $y^2=138 x^6+75 x^5+88 x^4+55 x^3+x^2+128 x+79$
• $y^2=7 x^6+42 x^4+37 x^3+141 x^2+86 x+89$
• $y^2=8 x^6+66 x^5+66 x^4+33 x^3+93 x^2+86 x+76$
• $y^2=78 x^6+146 x^5+97 x^4+79 x^3+61 x^2+63 x+99$
• $y^2=48 x^6+3 x^5+37 x^4+12 x^3+47 x^2+139 x+62$
• $y^2=56 x^6+125 x^5+24 x^4+55 x^3+94 x^2+120 x+53$
• $y^2=60 x^6+78 x^5+67 x^4+67 x^3+45 x^2+32 x+38$
• $y^2=31 x^6+72 x^5+42 x^4+146 x^3+29 x^2+12 x+50$
• $y^2=82 x^6+139 x^5+138 x^4+107 x^3+31 x^2+110 x+90$
• $y^2=4 x^6+90 x^5+103 x^4+138 x^3+45 x^2+7 x+104$
• $y^2=75 x^6+75 x^5+2 x^4+125 x^3+106 x^2+102 x+27$
• $y^2=54 x^6+12 x^5+131 x^4+89 x^3+13 x^2+23 x+102$
• $y^2=124 x^6+132 x^5+63 x^4+78 x^3+132 x^2+28 x+87$
• $y^2=32 x^6+81 x^5+91 x^4+22 x^3+82 x^2+134 x+75$
• $y^2=96 x^6+107 x^5+64 x^4+67 x^3+45 x^2+62 x+29$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{149}$.

Endomorphism algebra over $\F_{149}$

The endomorphism algebra of this simple isogeny class is 4.0.4269740.2.

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
2.149.bp_bbg	$2$	(not in LMFDB)