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

• Label: 2.113.abb_ny
• 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:	$1 - 27 x + 362 x^{2} - 3051 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0959981567025$, $\pm0.397959623234$
Angle rank:	$2$ (numerical)
Number field:	4.0.555677100.1
Galois group:	$D_{4}$
Jacobians:	$64$
Isomorphism classes:	128

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10054$	$162975340$	$2082652962016$	$26581773399033600$	$339451425690157452694$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$87$	$12765$	$1443384$	$163030993$	$18424063407$	$2081951438370$	$235260587808879$	$26584442445595873$	$3004041940259697432$	$339456738992007161325$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 64 curves (of which all are hyperelliptic):

• $y^2=45 x^6+67 x^5+13 x^4+82 x^3+38 x^2+104 x+15$
• $y^2=7 x^6+101 x^5+101 x^4+26 x^3+104 x^2+56 x+6$
• $y^2=9 x^6+6 x^5+32 x^4+2 x^3+44 x^2+87 x+96$
• $y^2=47 x^6+67 x^5+27 x^4+65 x^3+42 x^2+92 x+96$
• $y^2=27 x^6+90 x^5+69 x^4+100 x^3+7 x^2+67 x+38$
• $y^2=94 x^6+5 x^5+18 x^4+58 x^3+79 x^2+97 x+101$
• $y^2=95 x^6+107 x^5+112 x^4+16 x^3+10 x^2+77 x+2$
• $y^2=70 x^6+112 x^5+68 x^4+111 x^3+10 x^2+80 x+21$
• $y^2=99 x^6+44 x^5+19 x^4+46 x^3+96 x^2+104 x+12$
• $y^2=45 x^6+73 x^5+103 x^4+38 x^3+40 x^2+79 x+4$
• $y^2=85 x^6+79 x^5+27 x^4+26 x^3+55 x^2+44 x+37$
• $y^2=59 x^6+81 x^5+63 x^4+26 x^3+16 x^2+78 x+63$
• $y^2=62 x^6+67 x^5+57 x^4+45 x^3+90 x^2+13 x+34$
• $y^2=84 x^6+67 x^5+23 x^4+103 x^3+100 x^2+95$
• $y^2=2 x^6+61 x^5+45 x^4+84 x^3+106 x^2+78 x+70$
• $y^2=19 x^6+24 x^5+63 x^4+58 x^3+98 x^2+90 x+97$
• $y^2=8 x^6+37 x^5+91 x^4+41 x^3+90 x^2+107 x+41$
• $y^2=71 x^6+28 x^5+83 x^3+11 x^2+82 x+58$
• $y^2=37 x^6+102 x^5+52 x^4+85 x^3+27 x^2+92 x+105$
• $y^2=69 x^6+42 x^5+3 x^4+46 x^3+47 x^2+56 x+65$
• and

• $y^2=87 x^6+22 x^5+84 x^4+44 x^3+22 x^2+96 x+110$
• $y^2=54 x^6+109 x^5+23 x^4+57 x^3+84 x^2+33 x+1$
• $y^2=71 x^6+17 x^5+73 x^4+11 x^3+24 x^2+43 x+70$
• $y^2=46 x^6+78 x^5+44 x^4+11 x^3+x^2+68 x+104$
• $y^2=29 x^6+58 x^5+3 x^4+29 x^3+108 x^2+59 x+18$
• $y^2=96 x^6+11 x^5+62 x^4+x^3+15 x^2+99 x+55$
• $y^2=42 x^6+71 x^5+46 x^4+17 x^3+29 x^2+47 x+17$
• $y^2=3 x^6+x^5+13 x^4+22 x^3+46 x^2+66 x+55$
• $y^2=89 x^6+32 x^5+107 x^4+66 x^3+51 x^2+13 x+110$
• $y^2=50 x^5+28 x^4+17 x^3+99 x^2+24 x+90$
• $y^2=35 x^6+17 x^5+26 x^4+104 x^3+69 x^2+13 x+70$
• $y^2=25 x^6+106 x^5+7 x^4+15 x^3+74 x^2+13 x+18$
• $y^2=6 x^6+59 x^5+17 x^4+52 x^3+76 x^2+104 x+47$
• $y^2=79 x^6+49 x^5+16 x^4+109 x^3+88 x^2+50 x+75$
• $y^2=103 x^6+81 x^5+101 x^4+65 x^3+81 x^2+110 x+34$
• $y^2=33 x^6+16 x^5+85 x^4+103 x^3+89 x^2+112 x+38$
• $y^2=33 x^6+103 x^5+23 x^4+34 x^3+57 x^2+95 x+68$
• $y^2=26 x^6+80 x^5+5 x^4+107 x^3+37 x^2+52 x+6$
• $y^2=81 x^6+73 x^5+78 x^4+20 x^3+74 x^2+40 x+69$
• $y^2=x^6+55 x^5+49 x^4+8 x^3+53 x^2+40 x+27$
• $y^2=89 x^6+111 x^5+81 x^4+12 x^3+26 x^2+97 x+29$
• $y^2=42 x^6+x^5+37 x^4+35 x^3+99 x^2+110 x+94$
• $y^2=76 x^6+57 x^5+69 x^4+7 x^3+59 x^2+13 x+96$
• $y^2=21 x^6+51 x^5+70 x^4+2 x^3+85 x^2+3 x+88$
• $y^2=27 x^6+54 x^5+101 x^4+90 x^3+32 x^2+103 x+38$
• $y^2=84 x^6+51 x^5+101 x^4+90 x^3+98 x^2+102 x+105$
• $y^2=112 x^6+13 x^5+36 x^4+109 x^3+66 x^2+61 x+35$
• $y^2=70 x^6+5 x^5+9 x^4+47 x^3+32 x^2+41 x+92$
• $y^2=107 x^6+56 x^5+58 x^4+3 x^3+5 x^2+109 x+3$
• $y^2=25 x^6+12 x^5+65 x^4+15 x^3+49 x^2+95 x+81$
• $y^2=45 x^6+17 x^5+41 x^4+63 x^3+15 x^2+58 x+74$
• $y^2=62 x^6+16 x^5+81 x^4+28 x^3+36 x^2+59 x+3$
• $y^2=92 x^6+13 x^5+30 x^4+52 x^3+86 x^2+8 x+12$
• $y^2=28 x^6+72 x^5+66 x^4+77 x^3+88 x^2+87 x+40$
• $y^2=102 x^6+19 x^5+34 x^4+47 x^3+35 x^2+101 x+85$
• $y^2=x^6+54 x^5+73 x^4+106 x^3+23 x^2+94 x+84$
• $y^2=18 x^6+33 x^5+104 x^4+29 x^3+42 x^2+4 x+63$
• $y^2=12 x^6+38 x^5+94 x^4+46 x^3+108 x^2+3 x+86$
• $y^2=74 x^6+65 x^5+97 x^3+20 x^2+105 x+52$
• $y^2=87 x^6+53 x^5+72 x^4+2 x^3+78 x^2+7 x+46$
• $y^2=27 x^6+99 x^5+4 x^4+16 x^3+5 x^2+33 x+61$
• $y^2=29 x^6+2 x^5+22 x^4+112 x^3+104 x^2+46 x+61$
• $y^2=110 x^6+39 x^5+26 x^4+39 x^3+16 x^2+74 x+9$
• $y^2=95 x^6+18 x^5+65 x^4+7 x^3+68 x^2+94 x+37$

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 4.0.555677100.1.

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_ny	$2$	(not in LMFDB)