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

• Label: 2.113.abb_ok
• 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:	$1 - 27 x + 374 x^{2} - 3051 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.135883189855$, $\pm0.382873852844$
Angle rank:	$2$ (numerical)
Number field:	4.0.4729788.1
Galois group:	$D_{4}$
Jacobians:	$44$
Isomorphism classes:	44

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10066$	$163290652$	$2084056909312$	$26584598608795584$	$339454589477261669026$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$87$	$12789$	$1444356$	$163048321$	$18424235127$	$2081952449682$	$235260594807927$	$26584442562766849$	$3004041941221321332$	$339456738976391335509$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 44 curves (of which all are hyperelliptic):

• $y^2=93 x^6+77 x^5+44 x^4+75 x^3+38 x^2+x+58$
• $y^2=39 x^6+43 x^5+91 x^4+25 x^3+63 x^2+9 x+55$
• $y^2=12 x^6+29 x^5+30 x^4+86 x^3+111 x^2+36 x+59$
• $y^2=70 x^6+53 x^5+56 x^4+95 x^3+102 x^2+46 x+99$
• $y^2=108 x^6+111 x^5+14 x^4+93 x^3+76 x^2+30 x+46$
• $y^2=65 x^6+44 x^5+110 x^4+27 x^3+48 x^2+36 x+63$
• $y^2=24 x^6+105 x^5+45 x^4+69 x^3+25 x^2+105 x+112$
• $y^2=42 x^6+71 x^5+80 x^4+88 x^3+27 x^2+93 x+45$
• $y^2=16 x^6+73 x^5+31 x^4+53 x^3+32 x^2+16 x+35$
• $y^2=76 x^6+94 x^5+5 x^4+10 x^3+16 x^2+48 x+104$
• $y^2=75 x^6+100 x^5+12 x^4+86 x^3+7 x^2+69 x+107$
• $y^2=70 x^6+15 x^5+70 x^4+56 x^3+77 x^2+99 x+37$
• $y^2=111 x^6+111 x^5+15 x^4+49 x^3+70 x^2+56 x+6$
• $y^2=47 x^6+99 x^5+67 x^4+65 x^3+27 x^2+64 x+12$
• $y^2=74 x^6+39 x^5+48 x^4+30 x^3+22 x^2+x+112$
• $y^2=101 x^6+65 x^5+65 x^4+48 x^3+56 x^2+74 x+107$
• $y^2=50 x^6+110 x^5+93 x^4+13 x^3+70 x^2+104 x+31$
• $y^2=36 x^6+64 x^5+63 x^4+85 x^3+12 x^2+53 x+37$
• $y^2=2 x^6+42 x^5+59 x^4+84 x^3+50 x^2+30 x+37$
• $y^2=98 x^6+9 x^5+48 x^4+59 x^3+56 x^2+12 x+68$
• and

• $y^2=82 x^6+70 x^5+71 x^4+94 x^3+104 x^2+27 x+42$
• $y^2=10 x^6+79 x^5+72 x^4+x^3+6 x^2+84 x+66$
• $y^2=15 x^6+54 x^5+104 x^4+36 x^3+110 x^2+108 x+68$
• $y^2=75 x^6+2 x^5+85 x^4+17 x^3+84 x^2+12 x+45$
• $y^2=91 x^6+97 x^5+x^4+88 x^3+39 x^2+66 x+48$
• $y^2=108 x^6+7 x^5+11 x^4+75 x^3+86 x^2+93 x+89$
• $y^2=93 x^6+106 x^5+106 x^4+25 x^2+69 x+15$
• $y^2=12 x^6+68 x^4+101 x^3+50 x^2+53 x+66$
• $y^2=66 x^6+97 x^5+6 x^4+50 x^3+9 x^2+22 x+54$
• $y^2=82 x^6+59 x^5+19 x^4+16 x^3+63 x^2+24 x+30$
• $y^2=101 x^6+82 x^5+35 x^4+101 x^3+78 x^2+63 x+54$
• $y^2=10 x^6+18 x^5+111 x^4+27 x^3+74 x^2+11 x+22$
• $y^2=111 x^6+22 x^5+30 x^4+92 x^3+51 x^2+108 x+10$
• $y^2=7 x^6+40 x^5+30 x^4+28 x^3+95 x^2+72 x+79$
• $y^2=49 x^6+88 x^5+60 x^4+83 x^3+95 x^2+85 x+10$
• $y^2=104 x^6+95 x^5+11 x^4+86 x^2+106 x+24$
• $y^2=111 x^6+93 x^5+21 x^4+76 x^3+58 x^2+78 x+90$
• $y^2=62 x^6+2 x^5+8 x^4+94 x^3+68 x^2+93 x+73$
• $y^2=68 x^6+2 x^5+6 x^4+70 x^3+90 x^2+69 x+4$
• $y^2=76 x^6+12 x^4+59 x^3+88 x^2+68 x+56$
• $y^2=19 x^6+18 x^5+13 x^4+93 x^3+16 x^2+12 x+72$
• $y^2=63 x^6+74 x^5+46 x^4+68 x^3+95 x^2+14 x+59$
• $y^2=40 x^6+15 x^5+10 x^4+59 x^3+60 x^2+41 x+38$
• $y^2=102 x^6+37 x^5+3 x^4+9 x^3+82 x^2+50 x+29$

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 4.0.4729788.1.

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_ok	$2$	(not in LMFDB)