Abelian variety isogeny class 2.137.abo_zq over $\F_{137}$

• Label: 2.137.abo_zq
• Base field: $\F_{137}$
• 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:	$\F_{137}$
Dimension:	$2$
L-polynomial:	$1 - 40 x + 666 x^{2} - 5480 x^{3} + 18769 x^{4}$
Frobenius angles:	$\pm0.0710640823629$, $\pm0.237869879993$
Angle rank:	$2$ (numerical)
Number field:	4.0.27200.2
Galois group:	$D_{4}$
Jacobians:	$44$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$13916$	$347287696$	$6610519275164$	$124102708061889536$	$2329202300344601817436$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$98$	$18502$	$2570834$	$352288926$	$48261895458$	$6611856237478$	$905824276012754$	$124097929446096318$	$17001416401620954338$	$2329194047586806054022$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 44 curves (of which all are hyperelliptic):

• $y^2=54 x^6+49 x^5+76 x^4+86 x^3+87 x^2+112 x+60$
• $y^2=102 x^6+18 x^5+134 x^4+20 x^3+43 x^2+118 x+43$
• $y^2=110 x^6+128 x^5+39 x^4+41 x^3+37 x^2+84 x+134$
• $y^2=118 x^6+95 x^5+27 x^4+60 x^3+125 x^2+46 x+128$
• $y^2=20 x^6+103 x^5+101 x^4+86 x^3+35 x^2+60 x+26$
• $y^2=126 x^6+50 x^5+67 x^4+55 x^3+127 x^2+99 x+17$
• $y^2=130 x^6+93 x^5+130 x^4+131 x^3+111 x^2+10 x+5$
• $y^2=83 x^6+33 x^5+118 x^4+135 x^3+x^2+96 x+133$
• $y^2=42 x^6+48 x^5+5 x^4+98 x^3+99 x^2+59 x+106$
• $y^2=17 x^6+62 x^5+118 x^4+63 x^3+80 x^2+54 x+118$
• $y^2=51 x^6+113 x^5+43 x^4+20 x^3+9 x^2+7 x+120$
• $y^2=49 x^6+85 x^5+35 x^4+44 x^3+132 x^2+127 x+66$
• $y^2=126 x^6+71 x^5+48 x^4+64 x^3+12 x^2+111 x+134$
• $y^2=54 x^6+63 x^5+45 x^4+35 x^3+109 x^2+112 x+27$
• $y^2=82 x^6+37 x^5+20 x^4+74 x^3+27 x^2+x+27$
• $y^2=132 x^6+102 x^5+39 x^4+14 x^3+36 x^2+54 x+57$
• $y^2=44 x^6+70 x^5+66 x^4+60 x^3+129 x^2+53 x+79$
• $y^2=26 x^6+50 x^5+111 x^4+22 x^3+105 x^2+114 x+77$
• $y^2=119 x^6+13 x^5+89 x^4+38 x^3+15 x^2+51 x+80$
• $y^2=117 x^6+58 x^5+74 x^4+98 x^3+87 x^2+23 x+87$
• and

• $y^2=21 x^6+131 x^5+111 x^4+136 x^3+7 x^2+72 x+13$
• $y^2=134 x^6+46 x^5+111 x^4+33 x^3+8 x^2+123 x+80$
• $y^2=13 x^6+105 x^5+73 x^4+81 x^3+84 x^2+76 x+52$
• $y^2=72 x^6+101 x^5+74 x^4+78 x^3+106 x^2+67 x+104$
• $y^2=20 x^6+122 x^5+105 x^4+14 x^3+35 x^2+16 x+99$
• $y^2=134 x^6+22 x^5+81 x^4+31 x^3+33 x^2+99 x+86$
• $y^2=77 x^6+3 x^5+120 x^4+48 x^3+54 x^2+124 x+12$
• $y^2=78 x^6+21 x^5+6 x^4+27 x^3+6 x^2+61 x+85$
• $y^2=64 x^6+126 x^5+26 x^4+94 x^3+119 x^2+74 x+40$
• $y^2=102 x^6+52 x^5+105 x^4+71 x^3+75 x^2+24 x+124$
• $y^2=52 x^6+49 x^5+60 x^4+52 x^3+82 x^2+46 x+106$
• $y^2=57 x^6+82 x^5+125 x^4+71 x^3+87 x^2+98 x+127$
• $y^2=40 x^6+4 x^5+47 x^4+13 x^3+64 x^2+32 x+127$
• $y^2=24 x^6+111 x^5+30 x^4+115 x^3+132 x^2+38 x+3$
• $y^2=94 x^6+85 x^5+108 x^4+11 x^3+58 x^2+62 x+102$
• $y^2=98 x^6+23 x^5+81 x^4+63 x^3+134 x^2+115 x+71$
• $y^2=23 x^6+45 x^5+111 x^4+31 x^3+127 x^2+102 x+97$
• $y^2=16 x^6+132 x^5+135 x^4+108 x^3+113 x^2+68 x+68$
• $y^2=73 x^6+85 x^5+98 x^4+28 x^3+98 x^2+13 x+60$
• $y^2=54 x^6+18 x^5+49 x^4+129 x^3+124 x^2+69 x+58$
• $y^2=6 x^6+2 x^5+61 x^4+103 x^3+111 x^2+5 x+38$
• $y^2=81 x^6+86 x^5+84 x^4+94 x^3+48 x^2+121 x+73$
• $y^2=95 x^6+20 x^5+104 x^4+63 x^3+55 x^2+40 x+117$
• $y^2=83 x^6+49 x^5+55 x^4+84 x^3+54 x^2+114 x+10$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{137}$.

Endomorphism algebra over $\F_{137}$

The endomorphism algebra of this simple isogeny class is 4.0.27200.2.

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
2.137.bo_zq	$2$	(not in LMFDB)