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

• Label: 2.149.abs_bdy
• Base field: $\F_{149}$
• 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:	$\F_{149}$
Dimension:	$2$
L-polynomial:	$( 1 - 24 x + 149 x^{2} )( 1 - 20 x + 149 x^{2} )$
	$1 - 44 x + 778 x^{2} - 6556 x^{3} + 22201 x^{4}$
Frobenius angles:	$\pm0.0586410025892$, $\pm0.194400112214$
Angle rank:	$2$ (numerical)
Jacobians:	$36$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$16380$	$484520400$	$10935398352060$	$242935582675968000$	$5393416233909565215900$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$106$	$21822$	$3305794$	$492885518$	$73439987786$	$10942529349582$	$1630436473192514$	$242935032483576478$	$36197319872170760746$	$5393400661958180801502$

Jacobians and polarizations

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

• $y^2=80 x^6+43 x^5+101 x^4+146 x^3+4 x^2+88 x+129$
• $y^2=21 x^6+128 x^5+123 x^4+45 x^3+113 x^2+77 x+8$
• $y^2=140 x^6+25 x^5+57 x^4+147 x^3+57 x^2+25 x+140$
• $y^2=103 x^6+129 x^5+48 x^4+110 x^3+38 x^2+63 x+16$
• $y^2=51 x^6+107 x^5+21 x^4+15 x^3+53 x^2+132 x+119$
• $y^2=38 x^6+64 x^5+12 x^4+102 x^3+12 x^2+64 x+38$
• $y^2=126 x^6+108 x^5+129 x^4+21 x^3+90 x^2+98 x+39$
• $y^2=82 x^6+81 x^5+123 x^4+112 x^3+118 x^2+44 x+131$
• $y^2=35 x^6+127 x^5+145 x^4+139 x^3+121 x^2+99 x+46$
• $y^2=93 x^6+93 x^5+81 x^4+141 x^3+113 x^2+99 x+102$
• $y^2=106 x^6+68 x^5+147 x^4+130 x^3+147 x^2+34 x+15$
• $y^2=90 x^6+113 x^5+118 x^4+23 x^3+118 x^2+113 x+90$
• $y^2=24 x^6+67 x^5+43 x^4+52 x^3+43 x^2+67 x+24$
• $y^2=2 x^6+40 x^5+72 x^4+41 x^2+90 x+105$
• $y^2=16 x^6+11 x^5+26 x^4+119 x^3+92 x^2+9 x+140$
• $y^2=34 x^6+89 x^5+76 x^4+114 x^3+40 x^2+22 x+110$
• $y^2=44 x^6+130 x^5+93 x^4+117 x^3+93 x^2+130 x+44$
• $y^2=113 x^6+8 x^5+72 x^4+56 x^3+41 x^2+18 x+47$
• $y^2=86 x^6+126 x^5+26 x^4+124 x^3+5 x^2+58 x+46$
• $y^2=22 x^6+45 x^5+142 x^4+120 x^3+142 x^2+45 x+22$
• and

• $y^2=20 x^6+81 x^5+148 x^4+18 x^3+148 x^2+81 x+20$
• $y^2=143 x^6+110 x^5+11 x^4+67 x^3+135 x^2+124 x+82$
• $y^2=115 x^6+129 x^5+67 x^4+47 x^3+67 x^2+129 x+115$
• $y^2=34 x^6+88 x^5+112 x^4+148 x^3+40 x^2+109 x+79$
• $y^2=110 x^6+50 x^5+77 x^4+53 x^3+98 x^2+74 x+62$
• $y^2=141 x^6+80 x^5+126 x^4+116 x^3+117 x^2+145 x+77$
• $y^2=109 x^6+54 x^5+6 x^4+28 x^3+26 x^2+120 x+32$
• $y^2=123 x^6+74 x^5+7 x^4+59 x^3+104 x^2+129 x+48$
• $y^2=40 x^6+128 x^5+127 x^4+110 x^3+97 x^2+51 x+146$
• $y^2=114 x^6+144 x^5+13 x^4+61 x^3+93 x^2+110 x+127$
• $y^2=94 x^6+x^5+138 x^4+104 x^3+72 x^2+124 x+74$
• $y^2=70 x^6+68 x^5+110 x^4+26 x^3+98 x^2+125 x+65$
• $y^2=24 x^6+89 x^5+25 x^4+48 x^3+25 x^2+89 x+24$
• $y^2=82 x^6+59 x^5+57 x^4+82 x^3+97 x^2+37 x+25$
• $y^2=145 x^6+56 x^5+146 x^4+76 x^3+106 x^2+65 x+86$
• $y^2=18 x^6+100 x^5+35 x^4+12 x^3+35 x^2+100 x+18$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{149}$

The isogeny class factors as 1.149.ay $\times$ 1.149.au and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.149.ay : \(\Q(\sqrt{-5}) \).
• 1.149.au : \(\Q(\sqrt{-1}) \).

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
2.149.ae_aha	$2$	(not in LMFDB)
2.149.e_aha	$2$	(not in LMFDB)
2.149.bs_bdy	$2$	(not in LMFDB)