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

• Label: 2.113.abb_pd
• 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:	$1 - 27 x + 393 x^{2} - 3051 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.194712791181$, $\pm0.350958666655$
Angle rank:	$2$ (numerical)
Number field:	4.0.199642813.1
Galois group:	$D_{4}$
Jacobians:	$37$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10085$	$163790485$	$2086280490845$	$26588880064281925$	$339458133847188204800$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$87$	$12827$	$1445895$	$163074579$	$18424427502$	$2081951516459$	$235260556685871$	$26584442138631331$	$3004041938559431535$	$339456738954771153182$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 37 curves (of which all are hyperelliptic):

• $y^2=54 x^6+102 x^5+77 x^4+43 x^3+28 x^2+52 x+112$
• $y^2=86 x^6+77 x^5+6 x^4+46 x^3+63 x^2+5 x+78$
• $y^2=71 x^6+70 x^5+107 x^4+79 x^3+58 x^2+3 x+33$
• $y^2=65 x^6+39 x^5+72 x^4+34 x^3+21 x^2+93 x+83$
• $y^2=73 x^6+18 x^5+19 x^4+98 x^3+95 x^2+103 x+77$
• $y^2=67 x^6+91 x^5+84 x^4+97 x^3+110 x^2+19 x+35$
• $y^2=98 x^6+2 x^5+52 x^4+86 x^3+27 x^2+95 x+45$
• $y^2=19 x^6+50 x^5+9 x^4+106 x^3+48 x^2+15 x+50$
• $y^2=6 x^6+108 x^5+67 x^4+56 x^3+19 x^2+108 x+108$
• $y^2=52 x^6+67 x^5+56 x^4+42 x^3+103 x^2+55 x+31$
• $y^2=3 x^6+110 x^5+102 x^4+91 x^3+34 x^2+98 x+25$
• $y^2=93 x^6+40 x^5+108 x^4+50 x^3+15 x^2+56 x+32$
• $y^2=57 x^6+101 x^5+43 x^4+29 x^3+18 x^2+38 x+63$
• $y^2=77 x^6+x^5+5 x^4+68 x^3+107 x^2+49 x+38$
• $y^2=13 x^6+3 x^5+93 x^4+13 x^3+23 x^2+28 x+67$
• $y^2=12 x^6+92 x^5+3 x^4+80 x^3+95 x^2+96 x+69$
• $y^2=80 x^6+84 x^4+24 x^3+80 x^2+x+110$
• $y^2=76 x^6+83 x^5+19 x^4+99 x^3+20 x^2+45 x+48$
• $y^2=9 x^6+102 x^5+21 x^4+96 x^3+19 x^2+73 x+85$
• $y^2=107 x^6+103 x^5+86 x^4+35 x^3+39 x^2+96 x+73$
• and

• $y^2=32 x^6+67 x^5+17 x^4+9 x^3+45 x^2+49 x+63$
• $y^2=45 x^6+78 x^5+71 x^4+13 x^3+111 x^2+80 x+100$
• $y^2=23 x^6+65 x^5+71 x^4+70 x^3+72 x^2+84 x+20$
• $y^2=68 x^6+36 x^5+67 x^4+105 x^3+92 x^2+44 x+54$
• $y^2=23 x^6+32 x^5+74 x^4+25 x^3+14 x^2+38 x+110$
• $y^2=24 x^6+103 x^5+37 x^4+78 x^3+81 x^2+12 x$
• $y^2=79 x^6+81 x^5+72 x^4+17 x^3+111 x^2+33 x+58$
• $y^2=30 x^6+88 x^5+7 x^4+97 x^3+45 x^2+109 x+4$
• $y^2=44 x^6+51 x^5+21 x^4+58 x^3+29 x^2+31 x+90$
• $y^2=x^6+23 x^5+21 x^4+64 x^3+66 x^2+14 x+80$
• $y^2=15 x^6+7 x^5+49 x^4+20 x^3+78 x^2+108 x+102$
• $y^2=55 x^6+36 x^5+14 x^4+83 x^3+41 x^2+56 x+104$
• $y^2=93 x^6+80 x^5+32 x^4+104 x^3+17 x^2+4 x+80$
• $y^2=78 x^6+32 x^5+36 x^4+72 x^3+69 x^2+11 x+95$
• $y^2=66 x^6+39 x^5+28 x^4+64 x^3+41 x^2+77 x+12$
• $y^2=50 x^6+29 x^5+33 x^4+40 x^3+71 x^2+67 x+58$
• $y^2=38 x^6+61 x^5+38 x^4+21 x^3+25 x^2+13 x+111$

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 4.0.199642813.1.

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_pd	$2$	(not in LMFDB)