Abelian variety isogeny class 2.113.abb_oh over $\F_{113}$

• Label: 2.113.abb_oh
• Base field: $\F_{113}$
• 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:	$\F_{113}$
Dimension:	$2$
L-polynomial:	$1 - 27 x + 371 x^{2} - 3051 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.126504360297$, $\pm0.386890610251$
Angle rank:	$2$ (numerical)
Number field:	4.0.12188349.2
Galois group:	$D_{4}$
Jacobians:	$72$
Isomorphism classes:	72

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10063$	$163211797$	$2083705892599$	$26583901099129269$	$339453865685386014448$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$87$	$12783$	$1444113$	$163044043$	$18424195842$	$2081952314223$	$235260595425957$	$26584442566567411$	$3004041941323281459$	$339456738983250643518$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 72 curves (of which all are hyperelliptic):

• $y^2=101 x^6+26 x^5+81 x^3+66 x^2+36 x+88$
• $y^2=108 x^6+43 x^5+104 x^4+48 x^3+78 x^2+81 x+5$
• $y^2=63 x^5+33 x^4+8 x^3+88 x^2+63 x+92$
• $y^2=27 x^6+55 x^5+91 x^4+81 x^3+x^2+61 x+103$
• $y^2=86 x^6+13 x^5+31 x^4+35 x^3+111 x^2+54 x+33$
• $y^2=43 x^6+36 x^5+68 x^4+95 x^3+89 x^2+83 x+20$
• $y^2=99 x^6+19 x^5+78 x^4+76 x^3+66 x^2+29 x+102$
• $y^2=74 x^6+77 x^5+26 x^4+56 x^3+93 x^2+78 x+35$
• $y^2=72 x^6+4 x^5+102 x^4+92 x^3+67 x^2+43 x+14$
• $y^2=39 x^6+87 x^5+68 x^4+27 x^3+43 x^2+37 x+1$
• $y^2=46 x^6+75 x^5+89 x^4+76 x^3+33 x^2+107$
• $y^2=101 x^6+70 x^5+11 x^4+79 x^3+2 x^2+88 x+67$
• $y^2=41 x^6+67 x^5+64 x^4+89 x^3+68 x^2+110 x+59$
• $y^2=85 x^6+48 x^5+75 x^4+42 x^3+49 x^2+109 x+5$
• $y^2=80 x^6+19 x^5+104 x^4+72 x^3+19 x^2+58 x+22$
• $y^2=20 x^6+90 x^5+90 x^4+112 x^3+96 x^2+63 x+78$
• $y^2=29 x^6+52 x^5+99 x^4+8 x^3+18 x^2+21 x+74$
• $y^2=86 x^6+109 x^5+21 x^4+87 x^2+51 x+40$
• $y^2=83 x^6+70 x^5+88 x^4+111 x^3+108 x^2+75 x+45$
• $y^2=93 x^6+19 x^5+105 x^4+60 x^3+73 x^2+52 x+9$
• and

• $y^2=72 x^6+58 x^5+85 x^4+74 x^3+85 x^2+39 x+66$
• $y^2=5 x^6+73 x^5+62 x^4+106 x^3+106 x^2+62 x+86$
• $y^2=82 x^6+9 x^5+18 x^4+41 x^3+56 x^2+29 x+2$
• $y^2=50 x^6+109 x^5+99 x^4+64 x^3+71 x^2+67 x+36$
• $y^2=48 x^6+88 x^5+20 x^4+101 x^3+54 x^2+58 x+63$
• $y^2=30 x^6+71 x^5+59 x^4+70 x^3+48 x^2+65 x+67$
• $y^2=46 x^6+57 x^5+42 x^4+96 x^3+81 x^2+101 x+19$
• $y^2=64 x^6+6 x^5+60 x^4+42 x^3+39 x^2+108 x+39$
• $y^2=76 x^6+4 x^5+47 x^4+104 x^3+20 x^2+78 x+3$
• $y^2=65 x^6+9 x^5+94 x^4+48 x^3+101 x^2+90 x+34$
• $y^2=6 x^6+11 x^5+100 x^4+22 x^3+31 x^2+81 x+88$
• $y^2=46 x^6+87 x^5+94 x^4+55 x^3+54 x^2+34 x+6$
• $y^2=29 x^6+18 x^5+16 x^4+18 x^3+4 x^2+33 x+22$
• $y^2=71 x^6+51 x^5+42 x^4+50 x^3+76 x^2+17 x+88$
• $y^2=3 x^6+16 x^5+82 x^4+39 x^3+79 x^2+46 x+92$
• $y^2=73 x^6+29 x^5+91 x^4+80 x^3+73 x^2+84 x+89$
• $y^2=103 x^6+38 x^5+103 x^4+68 x^3+100 x^2+73 x+59$
• $y^2=57 x^6+2 x^5+70 x^4+67 x^3+21 x^2+47 x+101$
• $y^2=19 x^6+11 x^5+111 x^4+43 x^3+26 x^2+40 x+88$
• $y^2=94 x^6+75 x^5+88 x^4+69 x^3+19 x^2+91 x+44$
• $y^2=91 x^6+63 x^5+110 x^4+107 x^3+29 x^2+31 x+29$
• $y^2=107 x^6+68 x^5+70 x^4+68 x^3+39 x^2+31 x+72$
• $y^2=64 x^6+15 x^5+77 x^4+45 x^3+35 x^2+35 x+99$
• $y^2=13 x^6+39 x^5+5 x^4+53 x^3+62 x^2+9 x+42$
• $y^2=x^6+20 x^5+84 x^4+27 x^3+106 x^2+20 x+27$
• $y^2=107 x^6+67 x^5+51 x^4+45 x^3+102 x^2+29 x+84$
• $y^2=71 x^6+78 x^5+48 x^4+89 x^3+48 x^2+45 x+80$
• $y^2=32 x^6+13 x^5+87 x^4+5 x^3+89 x^2+67 x+83$
• $y^2=23 x^6+50 x^5+11 x^4+97 x^3+36 x^2+53$
• $y^2=x^6+42 x^5+34 x^4+63 x^3+45 x^2+68 x+45$
• $y^2=50 x^6+35 x^5+82 x^4+99 x^3+64 x^2+80 x+90$
• $y^2=45 x^6+14 x^5+63 x^4+65 x^3+24 x^2+9 x+11$
• $y^2=60 x^6+4 x^5+78 x^4+56 x^3+39 x^2+3 x+30$
• $y^2=13 x^6+60 x^5+106 x^4+47 x^3+91 x^2+56 x+6$
• $y^2=20 x^6+9 x^5+88 x^4+80 x^3+11 x^2+45 x+73$
• $y^2=26 x^6+13 x^5+56 x^4+5 x^3+55 x^2+57 x+73$
• $y^2=9 x^6+57 x^5+35 x^4+18 x^3+85 x^2+24 x+94$
• $y^2=18 x^6+59 x^5+2 x^4+78 x^3+39 x^2+16 x+94$
• $y^2=63 x^6+51 x^5+61 x^4+49 x^3+5 x^2+62 x+59$
• $y^2=23 x^6+89 x^5+50 x^4+74 x^3+105 x^2+93 x+34$
• $y^2=34 x^6+47 x^5+105 x^4+11 x^3+75 x^2+77 x+70$
• $y^2=20 x^6+75 x^5+69 x^4+104 x^3+47 x^2+30 x+79$
• $y^2=3 x^6+36 x^5+89 x^4+31 x^3+63 x^2+99 x+20$
• $y^2=24 x^6+31 x^5+17 x^4+93 x^3+68 x^2+61 x+25$
• $y^2=89 x^6+89 x^5+68 x^4+54 x^3+11 x^2+62 x+75$
• $y^2=34 x^6+101 x^5+21 x^4+92 x^3+66 x^2+23 x+23$
• $y^2=43 x^6+73 x^5+79 x^4+39 x^3+98 x^2+91 x+10$
• $y^2=101 x^6+92 x^5+8 x^4+78 x^3+54 x^2+101 x+7$
• $y^2=15 x^6+68 x^5+11 x^4+49 x^3+97 x^2+112 x+76$
• $y^2=16 x^6+56 x^5+39 x^4+73 x^3+8 x^2+52 x+66$
• $y^2=26 x^6+43 x^5+8 x^4+13 x^3+2 x^2+7 x+54$
• $y^2=66 x^6+17 x^5+37 x^4+64 x^3+63 x^2+8 x+30$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{113}$.

Endomorphism algebra over $\F_{113}$

The endomorphism algebra of this simple isogeny class is 4.0.12188349.2.

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
2.113.bb_oh	$2$	(not in LMFDB)