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

• Label: 2.113.abb_oi
• 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:	$1 - 27 x + 372 x^{2} - 3051 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.129657785065$, $\pm0.385572403305$
Angle rank:	$2$ (numerical)
Number field:	4.0.36919900.1
Galois group:	$D_{4}$
Jacobians:	$84$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10064$	$163238080$	$2083822895936$	$26584134253638400$	$339454111923763803344$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$87$	$12785$	$1444194$	$163045473$	$18424209207$	$2081952368030$	$235260595391559$	$26584442567577793$	$3004041941309484162$	$339456738981072741425$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 84 curves (of which all are hyperelliptic):

• $y^2=17 x^6+44 x^5+2 x^4+99 x^3+99 x^2+29 x+57$
• $y^2=107 x^6+13 x^5+89 x^4+79 x^3+34 x^2+2 x+94$
• $y^2=39 x^6+43 x^5+105 x^4+96 x^3+42 x^2+98 x+101$
• $y^2=112 x^6+112 x^5+6 x^4+5 x^3+109 x^2+57 x+94$
• $y^2=105 x^6+11 x^5+103 x^4+39 x^3+13 x^2+59 x+93$
• $y^2=27 x^6+99 x^5+9 x^4+14 x^3+61 x^2+88 x+12$
• $y^2=74 x^6+83 x^5+23 x^4+100 x^3+99 x^2+48 x+89$
• $y^2=50 x^6+54 x^5+44 x^4+107 x^3+28 x^2+105 x+107$
• $y^2=9 x^6+3 x^4+39 x^3+92 x^2+6 x+44$
• $y^2=89 x^6+59 x^5+8 x^4+61 x^3+x^2+88 x+59$
• $y^2=9 x^6+83 x^5+19 x^4+107 x^3+22 x^2+36 x+18$
• $y^2=93 x^6+81 x^5+45 x^4+95 x^3+105 x^2+43 x+17$
• $y^2=5 x^6+89 x^5+9 x^4+86 x^3+x^2+110 x+5$
• $y^2=71 x^6+39 x^5+73 x^4+73 x^3+79 x^2+8 x+99$
• $y^2=44 x^6+6 x^5+3 x^4+34 x^3+13 x^2+7 x+39$
• $y^2=105 x^6+102 x^5+17 x^4+18 x^3+90 x^2+24 x+101$
• $y^2=5 x^6+15 x^5+14 x^4+53 x^3+32 x^2+48 x+55$
• $y^2=45 x^6+4 x^5+94 x^4+60 x^3+18 x^2+105 x$
• $y^2=78 x^6+71 x^5+37 x^4+97 x^3+36 x^2+99 x+84$
• $y^2=40 x^6+31 x^5+19 x^4+31 x^3+32 x^2+42 x+42$
• and

• $y^2=69 x^6+36 x^5+50 x^4+105 x^3+82 x^2+79 x+23$
• $y^2=x^6+51 x^5+78 x^4+103 x^3+93 x^2+53 x+68$
• $y^2=105 x^6+109 x^5+51 x^4+92 x^3+91 x^2+11 x+39$
• $y^2=103 x^6+61 x^5+47 x^4+49 x^3+77 x^2+98 x+70$
• $y^2=100 x^6+76 x^5+57 x^4+63 x^3+16 x^2+48 x+68$
• $y^2=91 x^6+56 x^5+90 x^4+47 x^3+29 x^2+75 x+68$
• $y^2=7 x^6+95 x^5+50 x^4+106 x^3+56 x^2+7 x+80$
• $y^2=25 x^6+x^5+26 x^4+20 x^3+81 x^2+111 x+59$
• $y^2=54 x^6+13 x^5+51 x^4+66 x^3+54 x^2+65 x+21$
• $y^2=15 x^6+53 x^5+14 x^4+21 x^3+58 x^2+77 x+79$
• $y^2=34 x^6+62 x^5+59 x^4+19 x^3+47 x^2+65 x+29$
• $y^2=74 x^6+73 x^5+38 x^4+87 x^3+77 x^2+94 x+70$
• $y^2=86 x^6+17 x^5+17 x^4+49 x^3+56 x^2+40 x+20$
• $y^2=105 x^6+61 x^5+106 x^4+111 x^3+62 x^2+42 x+54$
• $y^2=39 x^6+55 x^5+19 x^4+51 x^3+75 x^2+33 x+35$
• $y^2=109 x^6+68 x^5+14 x^4+48 x^3+5 x^2+27 x+35$
• $y^2=31 x^6+34 x^5+51 x^4+8 x^3+63 x^2+43 x+21$
• $y^2=109 x^6+72 x^5+62 x^4+33 x^3+104 x^2+44 x+16$
• $y^2=70 x^6+78 x^5+110 x^4+6 x^3+14 x^2+100 x+27$
• $y^2=12 x^6+73 x^5+46 x^4+8 x^3+25 x^2+2 x+45$
• $y^2=84 x^6+68 x^5+29 x^4+96 x^3+82 x^2+95 x+9$
• $y^2=77 x^6+70 x^5+54 x^4+79 x^3+72 x^2+55 x+76$
• $y^2=54 x^6+32 x^5+102 x^4+9 x^3+2 x^2+72 x+37$
• $y^2=73 x^6+32 x^5+14 x^4+101 x^3+10 x^2+37 x+67$
• $y^2=46 x^6+38 x^5+84 x^4+107 x^3+11 x^2+35 x+4$
• $y^2=16 x^6+87 x^5+45 x^3+x^2+x+55$
• $y^2=3 x^6+72 x^5+99 x^4+27 x^3+57 x^2+6 x+33$
• $y^2=21 x^6+70 x^5+78 x^4+112 x^3+15 x^2+96 x+17$
• $y^2=5 x^6+72 x^5+40 x^4+77 x^3+91 x^2+3 x+48$
• $y^2=7 x^6+2 x^5+3 x^4+79 x^3+93 x^2+26 x+17$
• $y^2=41 x^6+84 x^5+104 x^4+62 x^3+78 x^2+42 x+48$
• $y^2=45 x^6+70 x^5+58 x^4+30 x^3+8 x^2+44 x+45$
• $y^2=50 x^6+46 x^5+20 x^4+19 x^3+8 x^2+106 x+70$
• $y^2=106 x^5+88 x^4+43 x^3+100 x^2+56 x+55$
• $y^2=32 x^6+23 x^5+34 x^4+45 x^3+52 x^2+77 x+10$
• $y^2=67 x^6+66 x^5+102 x^4+52 x^3+79 x^2+50 x+21$
• $y^2=21 x^6+75 x^5+2 x^4+85 x^3+3 x^2+31 x+38$
• $y^2=28 x^6+29 x^5+40 x^4+91 x^3+107 x^2+19 x+68$
• $y^2=12 x^6+73 x^5+39 x^4+94 x^3+69 x^2+60 x+29$
• $y^2=68 x^6+57 x^5+9 x^4+81 x^3+36 x^2+91 x+9$
• $y^2=84 x^6+21 x^4+43 x^3+94 x^2+37 x+33$
• $y^2=75 x^6+11 x^5+18 x^4+112 x^3+66 x^2+83 x+50$
• $y^2=110 x^6+98 x^5+45 x^4+78 x^3+25 x^2+103 x+4$
• $y^2=9 x^6+25 x^5+30 x^4+35 x^3+88 x^2+40 x+92$
• $y^2=93 x^6+85 x^5+35 x^4+101 x^3+76 x^2+3 x+103$
• $y^2=66 x^6+22 x^5+58 x^4+40 x^3+112 x^2+48 x+95$
• $y^2=77 x^6+64 x^5+102 x^4+81 x^3+69 x^2+58 x+84$
• $y^2=64 x^6+102 x^5+23 x^4+80 x^3+81 x^2+82 x+90$
• $y^2=86 x^6+90 x^5+75 x^4+79 x^3+91 x^2+24 x+50$
• $y^2=82 x^6+65 x^5+9 x^4+51 x^3+45 x^2+70 x+38$
• $y^2=36 x^6+42 x^5+46 x^4+53 x^3+62 x^2+6 x+99$
• $y^2=62 x^6+64 x^4+56 x^3+34 x^2+63 x+43$
• $y^2=51 x^6+81 x^5+41 x^4+62 x^3+5 x^2+7 x+111$
• $y^2=80 x^6+19 x^5+60 x^4+72 x^3+18 x^2+55 x+29$
• $y^2=7 x^6+59 x^5+72 x^4+54 x^3+46 x^2+19 x+87$
• $y^2=110 x^6+41 x^5+18 x^4+33 x^3+101 x+27$
• $y^2=2 x^6+4 x^5+4 x^4+100 x^3+7 x^2+34 x+2$
• $y^2=97 x^6+77 x^5+62 x^4+39 x^3+84 x^2+104 x+23$
• $y^2=35 x^6+43 x^5+49 x^4+29 x^3+73 x^2+66 x+3$
• $y^2=58 x^6+112 x^5+45 x^4+44 x^3+88 x^2+50 x+101$
• $y^2=74 x^6+65 x^5+52 x^4+70 x^3+40 x^2+103 x+38$
• $y^2=29 x^6+75 x^5+96 x^4+25 x^3+76 x^2+91 x+46$
• $y^2=101 x^6+27 x^5+74 x^4+7 x^3+86 x^2+58 x+44$
• $y^2=28 x^6+65 x^5+80 x^4+100 x^3+22 x^2+88 x+1$

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 4.0.36919900.1.

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_oi	$2$	(not in LMFDB)