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

• Label: 2.113.abb_ou
• 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:	$1 - 27 x + 384 x^{2} - 3051 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.166292695970$, $\pm0.367841913472$
Angle rank:	$2$ (numerical)
Number field:	4.0.827992.1
Galois group:	$D_{4}$
Jacobians:	$72$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10076$	$163553632$	$2085227111792$	$26586881309701504$	$339456678781051375676$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$87$	$12809$	$1445166$	$163062321$	$18424348527$	$2081952341822$	$235260581887887$	$26584442415590689$	$3004041939964143822$	$339456738954584385209$

Jacobians and polarizations

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

• $y^2=55 x^6+12 x^5+16 x^4+97 x^3+110 x^2+3 x+61$
• $y^2=57 x^6+105 x^5+61 x^4+19 x^3+72 x^2+97 x+83$
• $y^2=31 x^6+31 x^5+108 x^4+26 x^3+49 x^2+x+96$
• $y^2=62 x^6+15 x^5+112 x^4+84 x^3+95 x^2+46 x+50$
• $y^2=25 x^6+24 x^5+79 x^4+25 x^3+111 x^2+31 x+16$
• $y^2=73 x^6+102 x^5+19 x^4+83 x^3+28 x^2+35 x+35$
• $y^2=103 x^6+94 x^5+3 x^4+62 x^3+102 x^2+29 x+107$
• $y^2=17 x^6+38 x^5+24 x^4+17 x^3+46 x^2+112 x+101$
• $y^2=60 x^6+5 x^5+63 x^4+107 x^3+47 x^2+82 x+73$
• $y^2=82 x^6+94 x^5+76 x^4+112 x^3+48 x^2+x+80$
• $y^2=105 x^6+29 x^5+104 x^4+36 x^3+100 x^2+10 x+91$
• $y^2=3 x^6+107 x^5+98 x^4+3 x^3+10 x^2+37 x+102$
• $y^2=38 x^6+18 x^5+58 x^4+39 x^3+78 x^2+31 x+63$
• $y^2=45 x^6+37 x^5+10 x^4+33 x^3+102 x^2+75 x+34$
• $y^2=47 x^6+58 x^5+57 x^4+95 x^3+31 x^2+48 x+47$
• $y^2=14 x^6+22 x^5+13 x^4+11 x^3+2 x^2+53 x+74$
• $y^2=12 x^6+60 x^5+12 x^4+92 x^3+27 x^2+56 x+34$
• $y^2=101 x^6+28 x^5+7 x^4+16 x^3+18 x^2+20 x+72$
• $y^2=63 x^6+2 x^5+73 x^4+61 x^3+15 x^2+93 x+17$
• $y^2=84 x^6+72 x^5+63 x^4+49 x^3+40 x^2+76 x+48$
• and

• $y^2=93 x^6+14 x^5+25 x^4+43 x^3+43 x^2+20 x+110$
• $y^2=29 x^6+18 x^5+55 x^4+52 x^3+99 x^2+55 x+43$
• $y^2=110 x^6+60 x^5+56 x^4+104 x^3+14 x^2+109 x+9$
• $y^2=2 x^6+48 x^5+26 x^4+70 x^3+48 x^2+56 x+103$
• $y^2=106 x^6+4 x^5+22 x^4+70 x^3+57 x^2+6 x+86$
• $y^2=101 x^6+103 x^5+108 x^4+112 x^3+48 x^2+92 x+30$
• $y^2=53 x^6+70 x^5+71 x^4+78 x^3+20 x^2+21 x+38$
• $y^2=2 x^6+26 x^5+21 x^4+52 x^3+96 x^2+104 x+80$
• $y^2=101 x^6+4 x^5+104 x^4+57 x^3+59 x^2+66 x+15$
• $y^2=86 x^6+39 x^5+32 x^4+53 x^3+99 x^2+5 x+21$
• $y^2=82 x^6+45 x^5+104 x^4+71 x^3+90 x^2+14 x+43$
• $y^2=74 x^6+54 x^5+27 x^4+26 x^3+31 x^2+72 x+55$
• $y^2=38 x^6+83 x^5+16 x^4+83 x^3+70 x^2+10 x+4$
• $y^2=90 x^6+40 x^5+7 x^4+75 x^3+53 x^2+82 x+81$
• $y^2=31 x^6+72 x^5+55 x^4+88 x^3+x^2+34 x+92$
• $y^2=16 x^6+90 x^5+111 x^4+63 x^3+x^2+84 x+2$
• $y^2=98 x^6+41 x^5+39 x^4+46 x^3+21 x^2+29 x+111$
• $y^2=61 x^6+93 x^5+2 x^4+9 x^3+112 x^2+48 x+6$
• $y^2=40 x^6+67 x^5+102 x^4+84 x^3+68 x^2+60 x+21$
• $y^2=57 x^6+74 x^5+56 x^4+69 x^3+88 x^2+112 x+17$
• $y^2=63 x^6+111 x^5+61 x^4+99 x^3+82 x^2+67 x+37$
• $y^2=86 x^6+98 x^5+21 x^4+41 x^3+13 x^2+105 x+110$
• $y^2=41 x^6+26 x^5+5 x^4+100 x^3+98 x^2+68 x+76$
• $y^2=24 x^6+78 x^5+88 x^4+92 x^3+32 x^2+23 x+13$
• $y^2=87 x^6+4 x^5+96 x^4+66 x^3+79 x^2+85 x+79$
• $y^2=43 x^6+86 x^5+22 x^4+82 x^3+57 x^2+44 x+16$
• $y^2=26 x^6+5 x^5+9 x^4+16 x^3+30 x^2+39 x+60$
• $y^2=31 x^6+88 x^5+77 x^4+89 x^3+6 x^2+74 x+17$
• $y^2=34 x^6+14 x^5+84 x^4+26 x^3+70 x^2+69 x+8$
• $y^2=37 x^6+67 x^5+67 x^4+34 x^3+35 x^2+17 x+60$
• $y^2=33 x^6+17 x^5+97 x^4+x^3+105 x^2+57 x+76$
• $y^2=58 x^6+79 x^5+81 x^4+70 x^3+74 x^2+72 x+18$
• $y^2=89 x^6+54 x^5+58 x^4+21 x^3+34 x^2+86 x+105$
• $y^2=40 x^6+51 x^5+20 x^4+17 x^3+77 x^2+52 x+101$
• $y^2=10 x^6+3 x^5+102 x^4+67 x^3+25 x^2+19 x+20$
• $y^2=96 x^6+86 x^5+110 x^4+96 x^3+35 x^2+57 x+76$
• $y^2=65 x^6+23 x^5+41 x^4+70 x^3+77 x^2+85 x+32$
• $y^2=93 x^6+67 x^5+8 x^4+32 x^3+107 x^2+108 x+58$
• $y^2=19 x^6+79 x^5+81 x^4+2 x^3+110 x^2+58 x+66$
• $y^2=21 x^6+109 x^5+14 x^4+38 x^3+16 x^2+40 x+33$
• $y^2=80 x^6+86 x^5+101 x^4+2 x^3+40 x^2+9 x+90$
• $y^2=5 x^6+103 x^5+11 x^4+69 x^3+59 x^2+22 x+16$
• $y^2=23 x^6+17 x^5+18 x^4+59 x^3+19 x^2+4 x+103$
• $y^2=57 x^6+9 x^5+52 x^4+78 x^3+23 x^2+17 x+44$
• $y^2=50 x^6+27 x^5+92 x^4+72 x^3+28 x^2+5 x+2$
• $y^2=20 x^6+76 x^5+16 x^4+41 x^3+30 x^2+106 x+98$
• $y^2=108 x^6+109 x^5+55 x^4+95 x^3+2 x^2+58 x+50$
• $y^2=39 x^6+10 x^5+x^4+78 x^3+11 x^2+44 x+108$
• $y^2=90 x^6+23 x^5+21 x^4+23 x^3+17 x^2+107 x+1$
• $y^2=89 x^6+86 x^5+61 x^4+30 x^3+97 x^2+77 x+38$
• $y^2=23 x^6+112 x^5+32 x^4+33 x^2+29$
• $y^2=34 x^6+112 x^5+99 x^4+53 x^3+97 x^2+100 x+84$

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 4.0.827992.1.

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_ou	$2$	(not in LMFDB)