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

• Label: 2.113.abg_rq
• 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:	$1 - 32 x + 458 x^{2} - 3616 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0587677112590$, $\pm0.325130826324$
Angle rank:	$2$ (numerical)
Number field:	4.0.180288.2
Galois group:	$D_{4}$
Jacobians:	$44$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9580$	$161672080$	$2082457644460$	$26583804783232000$	$339451797782414761900$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$82$	$12662$	$1443250$	$163043454$	$18424083602$	$2081947612214$	$235260519758066$	$26584442000308606$	$3004041941672289490$	$339456739028192932982$

Jacobians and polarizations

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

• $y^2=59 x^6+58 x^5+38 x^4+110 x^3+71 x^2+55 x+12$
• $y^2=20 x^6+95 x^5+9 x^4+92 x^3+90 x^2+41 x+13$
• $y^2=54 x^6+29 x^5+41 x^4+40 x^3+10 x^2+58 x+92$
• $y^2=80 x^6+107 x^5+62 x^4+17 x^3+6 x^2+93 x+42$
• $y^2=75 x^6+83 x^5+94 x^4+33 x^3+103 x^2+50 x+95$
• $y^2=26 x^6+47 x^5+77 x^4+10 x^3+4 x^2+7 x+3$
• $y^2=94 x^6+34 x^5+68 x^4+72 x^3+26 x^2+34 x+16$
• $y^2=96 x^6+79 x^5+7 x^4+3 x^3+27 x^2+36 x+94$
• $y^2=58 x^6+13 x^5+67 x^4+25 x^3+60 x^2+35 x+108$
• $y^2=3 x^6+21 x^5+22 x^4+65 x^3+44 x^2+73 x+50$
• $y^2=24 x^6+104 x^5+75 x^4+26 x^3+92 x^2+101 x+34$
• $y^2=53 x^6+8 x^5+30 x^4+60 x^3+70 x^2+111 x+61$
• $y^2=80 x^6+32 x^5+42 x^4+51 x^3+47 x^2+64 x+58$
• $y^2=67 x^6+90 x^5+75 x^4+80 x^3+108 x^2+58 x+68$
• $y^2=40 x^6+9 x^5+109 x^4+12 x^3+13 x^2+28 x+34$
• $y^2=36 x^6+65 x^5+29 x^4+22 x^3+51 x^2+55 x+9$
• $y^2=95 x^6+9 x^5+37 x^4+75 x^3+108 x^2+89 x+112$
• $y^2=57 x^6+6 x^5+73 x^4+10 x^3+35 x^2+36 x+55$
• $y^2=56 x^6+30 x^5+31 x^4+66 x^3+80 x^2+87 x+105$
• $y^2=60 x^6+101 x^5+86 x^4+45 x^3+67 x^2+61 x+29$
• and

• $y^2=46 x^6+53 x^5+24 x^4+15 x^3+110 x^2+71 x+1$
• $y^2=60 x^6+32 x^5+82 x^4+26 x^3+22 x^2+59 x+17$
• $y^2=97 x^6+7 x^5+43 x^4+41 x^3+18 x^2+56 x+94$
• $y^2=4 x^6+14 x^5+5 x^4+29 x^3+22 x^2+73 x+58$
• $y^2=65 x^6+43 x^5+44 x^4+31 x^3+67 x^2+7 x+42$
• $y^2=48 x^6+58 x^5+65 x^4+89 x^3+28 x^2+45$
• $y^2=51 x^6+107 x^5+66 x^4+86 x^3+102 x^2+34 x+86$
• $y^2=73 x^6+x^5+102 x^4+32 x^3+19 x^2+20 x+65$
• $y^2=96 x^6+58 x^5+19 x^4+28 x^3+39 x^2+108 x+99$
• $y^2=74 x^6+61 x^5+111 x^4+86 x^3+50 x^2+73 x+90$
• $y^2=41 x^6+104 x^5+15 x^4+48 x^3+110 x^2+19 x+101$
• $y^2=71 x^6+28 x^5+52 x^4+44 x^3+108 x^2+24 x+108$
• $y^2=3 x^6+91 x^5+52 x^4+18 x^3+36 x^2+81 x+92$
• $y^2=81 x^6+33 x^5+56 x^4+55 x^3+3 x^2+22 x+62$
• $y^2=70 x^6+104 x^5+56 x^4+9 x^3+7 x^2+82 x+58$
• $y^2=8 x^6+67 x^5+83 x^4+107 x^3+82 x^2+9 x+60$
• $y^2=74 x^6+44 x^5+84 x^4+58 x^3+16 x^2+10 x+42$
• $y^2=68 x^6+107 x^5+40 x^4+14 x^3+72 x^2+49 x+102$
• $y^2=17 x^6+83 x^5+48 x^4+45 x^3+109 x^2+61 x+23$
• $y^2=90 x^6+68 x^5+94 x^4+7 x^3+111 x^2+56 x+99$
• $y^2=8 x^6+95 x^5+84 x^4+29 x^3+77 x^2+99 x+25$
• $y^2=34 x^6+35 x^5+12 x^4+65 x^3+17 x^2+4 x+78$
• $y^2=45 x^6+77 x^5+109 x^4+8 x^3+7 x^2+33 x+89$
• $y^2=85 x^6+51 x^5+91 x^4+2 x^3+7 x^2+56 x+94$

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 4.0.180288.2.

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.bg_rq	$2$	(not in LMFDB)