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

• Label: 2.113.abb_ot
• 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:	$1 - 27 x + 383 x^{2} - 3051 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.163251635001$, $\pm0.369484594205$
Angle rank:	$2$ (numerical)
Number field:	4.0.422045973.1
Galois group:	$D_{4}$
Jacobians:	$96$
Isomorphism classes:	96

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10075$	$163527325$	$2085110081275$	$26586655970077125$	$339456492235355326000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$87$	$12807$	$1445085$	$163060939$	$18424338402$	$2081952391119$	$235260583911321$	$26584442438687251$	$3004041940126310115$	$339456738956147441982$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 96 curves (of which all are hyperelliptic):

• $y^2=7 x^6+32 x^5+15 x^4+97 x^3+55 x^2+34 x+76$
• $y^2=33 x^6+46 x^5+24 x^4+105 x^3+13 x^2+85 x+16$
• $y^2=93 x^6+27 x^5+3 x^4+98 x^3+13 x^2+51 x+39$
• $y^2=36 x^6+31 x^4+8 x^3+8 x^2+19 x+23$
• $y^2=81 x^6+84 x^3+61 x^2+29 x+55$
• $y^2=99 x^6+65 x^5+64 x^4+73 x^3+87 x^2+78 x+60$
• $y^2=6 x^6+21 x^5+72 x^4+64 x^3+106 x^2+108 x+78$
• $y^2=49 x^6+9 x^5+87 x^4+27 x^3+49 x^2+21 x+51$
• $y^2=48 x^6+5 x^5+37 x^4+26 x^3+24 x^2+26 x+34$
• $y^2=75 x^6+7 x^5+57 x^4+100 x^3+2 x^2+106$
• $y^2=95 x^6+72 x^5+93 x^4+61 x^3+104 x^2+55 x+75$
• $y^2=42 x^6+47 x^5+108 x^4+43 x^3+86 x^2+50 x+55$
• $y^2=60 x^6+112 x^5+82 x^4+24 x^3+91 x^2+49 x+70$
• $y^2=9 x^6+20 x^5+5 x^4+78 x^3+35 x^2+105 x+6$
• $y^2=110 x^6+37 x^5+63 x^4+108 x^3+105 x^2+4 x+90$
• $y^2=78 x^6+111 x^5+73 x^4+30 x^3+18 x^2+19 x+4$
• $y^2=27 x^6+49 x^5+28 x^4+66 x^3+108 x^2+31 x+20$
• $y^2=3 x^6+10 x^5+108 x^4+50 x^3+67 x^2+67 x+74$
• $y^2=12 x^6+59 x^5+84 x^4+15 x^3+71 x^2+x+13$
• $y^2=20 x^6+18 x^5+99 x^4+96 x^3+60 x^2+51 x+93$
• and

• $y^2=98 x^6+5 x^5+112 x^4+56 x^3+56 x^2+57 x+48$
• $y^2=59 x^6+12 x^5+90 x^4+94 x^3+73 x^2+49 x+4$
• $y^2=28 x^6+63 x^5+40 x^4+9 x^3+107 x^2+45 x+69$
• $y^2=34 x^6+76 x^5+104 x^4+39 x^3+64 x^2+24 x+76$
• $y^2=4 x^6+35 x^5+22 x^4+36 x^3+30 x^2+51 x+8$
• $y^2=64 x^6+11 x^5+85 x^4+35 x^3+69 x^2+71 x+51$
• $y^2=29 x^6+112 x^5+105 x^4+14 x^3+72 x^2+102 x+5$
• $y^2=54 x^6+64 x^5+91 x^4+83 x^3+51 x^2+98 x+74$
• $y^2=65 x^6+50 x^5+12 x^4+110 x^3+18 x^2+83 x+88$
• $y^2=110 x^6+33 x^5+24 x^4+52 x^3+83 x^2+16 x+18$
• $y^2=52 x^6+3 x^5+45 x^4+7 x^3+28 x^2+72 x+84$
• $y^2=67 x^6+45 x^5+98 x^4+25 x^3+19 x^2+59 x+93$
• $y^2=21 x^6+66 x^5+9 x^4+15 x^3+15 x^2+75 x+109$
• $y^2=27 x^6+27 x^5+2 x^4+95 x^3+67 x^2+40 x+27$
• $y^2=26 x^6+34 x^5+84 x^4+84 x^3+62 x^2+47 x+42$
• $y^2=90 x^6+12 x^4+57 x^3+56 x^2+13 x+6$
• $y^2=24 x^6+84 x^5+25 x^4+22 x^3+x^2+85 x+103$
• $y^2=110 x^6+68 x^5+73 x^4+48 x^3+17 x^2+58 x+112$
• $y^2=58 x^6+x^5+36 x^4+22 x^3+66 x^2+83 x$
• $y^2=91 x^6+4 x^5+x^4+36 x^3+54 x^2+85 x+63$
• $y^2=32 x^6+60 x^5+80 x^4+3 x^3+85 x^2+12 x+84$
• $y^2=18 x^6+25 x^5+61 x^4+84 x^3+107 x^2+40 x+27$
• $y^2=79 x^6+106 x^5+30 x^4+111 x^2+91 x+37$
• $y^2=68 x^6+104 x^5+35 x^4+33 x^3+16 x^2+88 x+24$
• $y^2=75 x^6+93 x^5+28 x^4+112 x^3+57 x^2+53 x+25$
• $y^2=13 x^6+27 x^5+89 x^4+85 x^3+82 x^2+24 x+71$
• $y^2=60 x^6+107 x^5+20 x^4+36 x^3+49 x^2+60 x+39$
• $y^2=52 x^6+19 x^5+27 x^4+42 x^3+76 x^2+33 x+17$
• $y^2=13 x^6+37 x^5+62 x^4+70 x^3+27 x^2+99 x+29$
• $y^2=15 x^6+72 x^5+104 x^4+6 x^3+24 x^2+109 x+38$
• $y^2=24 x^6+99 x^5+88 x^4+90 x^3+5 x^2+74 x+16$
• $y^2=10 x^6+10 x^5+83 x^4+15 x^3+43 x^2+8 x+61$
• $y^2=70 x^6+11 x^5+61 x^4+98 x^3+47 x^2+20 x+26$
• $y^2=9 x^6+99 x^5+39 x^4+11 x^3+48 x^2+77 x+11$
• $y^2=98 x^6+99 x^5+18 x^4+8 x^3+44 x^2+46 x+86$
• $y^2=108 x^6+91 x^5+96 x^4+63 x^3+39 x+92$
• $y^2=9 x^6+99 x^5+41 x^4+101 x^3+52 x^2+66 x+111$
• $y^2=42 x^6+80 x^5+94 x^4+53 x^3+18 x^2+78 x+12$
• $y^2=110 x^6+62 x^5+94 x^4+99 x^3+20 x^2+84 x+57$
• $y^2=74 x^6+110 x^5+98 x^4+59 x^3+106 x^2+61 x+23$
• $y^2=106 x^6+99 x^5+7 x^4+43 x^3+43 x^2+25 x+86$
• $y^2=x^6+34 x^5+31 x^4+52 x^3+108 x^2+13 x+48$
• $y^2=81 x^6+60 x^5+57 x^4+60 x^3+33 x^2+78 x+78$
• $y^2=24 x^6+63 x^5+101 x^4+109 x^3+75 x^2+27 x+45$
• $y^2=23 x^6+63 x^5+86 x^4+82 x^3+5 x^2+42 x+63$
• $y^2=48 x^6+110 x^5+71 x^4+10 x^3+41 x^2+21 x+52$
• $y^2=107 x^6+96 x^5+44 x^4+17 x^3+34 x^2+52 x+75$
• $y^2=92 x^6+55 x^5+76 x^4+53 x^3+111 x^2+40 x+95$
• $y^2=54 x^6+95 x^5+40 x^4+93 x^3+98 x^2+60 x+49$
• $y^2=3 x^6+35 x^5+25 x^4+107 x^3+49 x^2+41 x$
• $y^2=101 x^6+36 x^5+82 x^4+102 x^3+53 x^2+67 x+87$
• $y^2=6 x^6+79 x^5+66 x^4+19 x^3+32 x^2+93 x+92$
• $y^2=6 x^6+81 x^5+74 x^4+33 x^3+84 x^2+45 x+110$
• $y^2=39 x^6+39 x^5+57 x^4+20 x^3+11 x^2+4 x+67$
• $y^2=35 x^6+72 x^5+81 x^4+17 x^3+8 x^2+39 x+75$
• $y^2=111 x^6+x^5+88 x^4+27 x^3+x^2+96 x+74$
• $y^2=46 x^6+72 x^5+16 x^4+30 x^3+106 x^2+16 x+109$
• $y^2=3 x^6+43 x^5+63 x^4+58 x^3+54 x^2+97 x+99$
• $y^2=45 x^6+16 x^5+61 x^4+99 x^3+69 x^2+80 x+20$
• $y^2=52 x^6+104 x^5+10 x^4+43 x^3+90 x^2+40 x+46$
• $y^2=90 x^6+66 x^5+30 x^4+71 x^3+3 x^2+21 x+38$
• $y^2=104 x^6+52 x^5+22 x^4+109 x^3+63 x^2+19 x+64$
• $y^2=85 x^6+67 x^5+75 x^4+96 x^3+98 x^2+39 x+38$
• $y^2=94 x^6+75 x^5+87 x^3+5 x^2+74 x+27$
• $y^2=79 x^6+30 x^5+67 x^4+64 x^3+23 x^2+89 x+73$
• $y^2=24 x^6+30 x^5+7 x^4+112 x^3+7 x^2+59 x+20$
• $y^2=42 x^6+52 x^5+57 x^4+56 x^3+70 x^2+52 x+45$
• $y^2=69 x^6+100 x^5+111 x^4+59 x^2+48 x+42$
• $y^2=4 x^6+48 x^5+7 x^4+106 x^3+x^2+102 x+38$
• $y^2=110 x^6+105 x^5+72 x^4+71 x^3+28 x^2+80 x+101$
• $y^2=103 x^6+65 x^5+98 x^4+95 x^3+16 x^2+59 x+96$
• $y^2=9 x^6+24 x^5+19 x^4+23 x^3+60 x^2+7 x+80$
• $y^2=93 x^6+11 x^5+87 x^4+35 x^3+44 x^2+40 x+74$
• $y^2=30 x^6+39 x^5+49 x^4+105 x^3+81 x^2+60 x+70$
• $y^2=65 x^6+13 x^5+80 x^4+43 x^3+34 x^2+27 x+17$
• $y^2=34 x^6+90 x^5+106 x^4+51 x^3+7 x^2+43 x+80$

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 4.0.422045973.1.

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_ot	$2$	(not in LMFDB)