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

• Label: 2.113.ay_od
• 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:	$1 - 24 x + 367 x^{2} - 2712 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.276481731221$, $\pm0.339560301288$
Angle rank:	$2$ (numerical)
Number field:	4.0.13146768.1
Galois group:	$D_{4}$
Jacobians:	$54$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10401$	$165095073$	$2088400689252$	$26590171678896969$	$339455633110286712801$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$90$	$12928$	$1447362$	$163082500$	$18424291770$	$2081947505254$	$235260506430522$	$26584441877638660$	$3004041941270116002$	$339456739031332396288$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 54 curves (of which all are hyperelliptic):

• $y^2=25 x^6+74 x^5+39 x^4+104 x^3+37 x^2+60 x+89$
• $y^2=50 x^6+48 x^5+15 x^4+80 x^3+110 x^2+55 x+55$
• $y^2=69 x^6+74 x^5+93 x^4+16 x^3+14 x^2+96 x+108$
• $y^2=14 x^6+106 x^5+94 x^4+75 x^3+77 x^2+32 x+50$
• $y^2=38 x^6+19 x^5+72 x^4+7 x^3+46 x^2+68 x+17$
• $y^2=55 x^6+28 x^5+58 x^4+64 x^3+65 x^2+24 x+71$
• $y^2=92 x^6+79 x^5+70 x^4+36 x^3+48 x^2+33 x+20$
• $y^2=70 x^6+65 x^5+19 x^4+70 x^3+55 x^2+32 x+94$
• $y^2=106 x^6+93 x^5+51 x^4+91 x^3+64 x^2+21 x+17$
• $y^2=92 x^6+9 x^5+35 x^4+55 x^3+49 x^2+98 x+111$
• $y^2=36 x^6+112 x^5+24 x^4+48 x^3+88 x^2+102 x+97$
• $y^2=42 x^6+61 x^5+57 x^4+20 x^3+40 x^2+12 x+2$
• $y^2=52 x^6+10 x^5+24 x^4+112 x^3+99 x^2+82 x+65$
• $y^2=25 x^6+62 x^5+74 x^4+93 x^3+112 x^2+96 x+23$
• $y^2=16 x^6+30 x^5+32 x^4+73 x^3+89 x^2+87 x+98$
• $y^2=45 x^6+21 x^5+38 x^4+80 x^3+31 x^2+31 x+33$
• $y^2=80 x^6+40 x^5+81 x^4+46 x^3+2 x^2+64 x+89$
• $y^2=59 x^6+13 x^5+102 x^4+50 x^3+83 x^2+75 x+62$
• $y^2=72 x^6+102 x^5+86 x^4+12 x^3+95 x^2+5 x+39$
• $y^2=27 x^6+46 x^5+39 x^4+2 x^2+99 x+33$
• and

• $y^2=94 x^6+86 x^5+73 x^4+84 x^3+22 x^2+45 x+109$
• $y^2=107 x^6+43 x^5+84 x^4+88 x^3+44 x^2+18 x+49$
• $y^2=59 x^6+90 x^5+73 x^4+79 x^3+21 x^2+106 x+89$
• $y^2=12 x^6+5 x^5+45 x^4+23 x^3+14 x^2+27 x+59$
• $y^2=108 x^6+57 x^5+44 x^4+48 x^3+87 x^2+39 x+39$
• $y^2=50 x^6+94 x^5+91 x^4+52 x^3+86 x^2+89 x+44$
• $y^2=96 x^6+56 x^5+68 x^4+46 x^3+76 x^2+13 x+35$
• $y^2=21 x^6+69 x^5+69 x^4+17 x^3+40 x^2+80 x+98$
• $y^2=92 x^6+3 x^5+22 x^4+22 x^3+82 x^2+36 x+18$
• $y^2=112 x^6+29 x^5+51 x^4+23 x^3+75 x^2+37 x+30$
• $y^2=76 x^6+107 x^5+72 x^4+35 x^3+105 x^2+109 x+26$
• $y^2=110 x^6+59 x^5+62 x^4+49 x^3+5 x+89$
• $y^2=3 x^6+71 x^5+56 x^4+61 x^3+55 x^2+70 x+46$
• $y^2=12 x^6+82 x^5+5 x^4+97 x^3+28 x^2+70 x+24$
• $y^2=112 x^6+16 x^5+110 x^4+20 x^3+46 x^2+103 x+70$
• $y^2=79 x^6+105 x^5+22 x^4+x^3+69 x^2+96 x+99$
• $y^2=35 x^6+58 x^5+45 x^4+106 x^3+74 x^2+48 x+104$
• $y^2=64 x^6+68 x^5+4 x^4+66 x^3+48 x^2+55 x+47$
• $y^2=72 x^6+17 x^5+90 x^4+102 x^3+33 x+107$
• $y^2=47 x^6+6 x^5+8 x^4+20 x^3+73 x^2+15 x+61$
• $y^2=23 x^6+43 x^5+32 x^4+9 x^3+96 x^2+33 x+94$
• $y^2=25 x^6+19 x^5+105 x^4+80 x^3+20 x^2+5 x+43$
• $y^2=27 x^6+35 x^5+111 x^4+28 x^3+90 x^2+6 x+56$
• $y^2=94 x^6+39 x^5+72 x^4+6 x^3+59 x^2+24 x+36$
• $y^2=97 x^6+104 x^5+12 x^4+72 x^3+106 x^2+91 x+19$
• $y^2=63 x^6+91 x^5+2 x^4+91 x^3+70 x^2+73 x+54$
• $y^2=47 x^6+56 x^5+4 x^4+104 x^3+99 x^2+10 x+10$
• $y^2=94 x^6+65 x^5+104 x^4+6 x^3+112 x^2+95 x+62$
• $y^2=67 x^6+58 x^5+24 x^4+50 x^3+93 x^2+x+75$
• $y^2=96 x^6+74 x^5+89 x^4+47 x^3+63 x^2+44 x+112$
• $y^2=6 x^6+82 x^5+90 x^4+91 x^3+80 x^2+9 x+43$
• $y^2=53 x^6+110 x^5+46 x^4+51 x^3+7 x^2+54 x+76$
• $y^2=4 x^6+49 x^5+59 x^4+28 x^3+48 x^2+33 x+8$
• $y^2=59 x^6+74 x^5+71 x^4+103 x^3+35 x^2+24 x+11$

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 4.0.13146768.1.

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.y_od	$2$	(not in LMFDB)