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

• Label: 2.113.au_hv
• 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:	$1 - 20 x + 203 x^{2} - 2260 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0402514335932$, $\pm0.516334722079$
Angle rank:	$2$ (numerical)
Number field:	4.0.784529424.1
Galois group:	$D_{4}$
Jacobians:	$36$
Isomorphism classes:	72

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10693$	$163100329$	$2078203925716$	$26576723825492281$	$339453973518779345293$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$94$	$12776$	$1440298$	$163000020$	$18424201694$	$2081952408422$	$235260517837838$	$26584441457078884$	$3004041938075338474$	$339456739013214924536$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 36 curves (of which all are hyperelliptic):

• $y^2=53 x^6+57 x^5+18 x^4+45 x^3+2 x^2+94 x+48$
• $y^2=17 x^6+8 x^5+67 x^4+16 x^3+26 x^2+9 x+7$
• $y^2=63 x^6+98 x^5+49 x^4+104 x^3+6 x^2+76 x+42$
• $y^2=3 x^6+107 x^5+25 x^4+5 x^3+96 x^2+5 x+50$
• $y^2=46 x^6+67 x^5+15 x^4+23 x^3+91 x^2+27 x+39$
• $y^2=29 x^6+109 x^5+69 x^4+111 x^3+x^2+97 x+101$
• $y^2=49 x^6+41 x^5+78 x^4+45 x^3+29 x^2+49 x+27$
• $y^2=56 x^6+72 x^5+103 x^4+36 x^3+3 x^2+71 x+69$
• $y^2=24 x^6+85 x^5+77 x^4+35 x^3+36 x^2+84 x+92$
• $y^2=18 x^6+60 x^5+23 x^4+44 x^3+12 x^2+47 x+30$
• $y^2=45 x^6+59 x^5+44 x^4+74 x^3+98 x^2+68 x+27$
• $y^2=107 x^6+20 x^5+58 x^4+18 x^3+74 x^2+17 x+75$
• $y^2=54 x^6+56 x^5+55 x^4+16 x^3+55 x^2+6 x+100$
• $y^2=11 x^6+111 x^5+43 x^4+77 x^3+78 x^2+9 x+91$
• $y^2=101 x^6+52 x^5+86 x^4+33 x^3+78 x^2+90 x+106$
• $y^2=59 x^6+25 x^5+72 x^4+16 x^3+83 x^2+14 x+37$
• $y^2=5 x^6+43 x^5+30 x^4+56 x^3+111 x^2+97 x+29$
• $y^2=88 x^6+62 x^5+97 x^4+22 x^3+4 x^2+80 x+45$
• $y^2=8 x^6+4 x^5+27 x^4+92 x^3+54 x^2+107 x+2$
• $y^2=89 x^6+37 x^5+32 x^4+53 x^3+52 x^2+87 x+27$
• and

• $y^2=111 x^6+47 x^5+94 x^4+32 x^3+27 x^2+62 x+32$
• $y^2=22 x^6+18 x^5+40 x^4+81 x^3+84 x^2+78 x+112$
• $y^2=11 x^6+101 x^5+16 x^4+34 x^3+44 x^2+90 x+105$
• $y^2=40 x^6+49 x^5+90 x^4+46 x^3+104 x^2+49 x+28$
• $y^2=41 x^6+63 x^5+69 x^4+76 x^3+51 x^2+98 x+101$
• $y^2=63 x^6+78 x^5+52 x^4+35 x^3+97 x^2+53 x+48$
• $y^2=92 x^6+73 x^5+61 x^4+51 x^3+70 x^2+79 x+94$
• $y^2=48 x^6+102 x^5+37 x^4+14 x^3+9 x^2+68 x+7$
• $y^2=74 x^6+108 x^5+111 x^4+5 x^3+100 x^2+42 x+41$
• $y^2=94 x^6+67 x^5+39 x^4+6 x^3+46 x^2+45 x+99$
• $y^2=108 x^6+96 x^5+59 x^4+70 x^3+46 x^2+44 x+32$
• $y^2=11 x^6+56 x^5+94 x^4+112 x^3+103 x^2+80 x+10$
• $y^2=41 x^6+112 x^5+15 x^4+45 x^3+31 x+31$
• $y^2=25 x^6+60 x^5+83 x^4+73 x^3+59 x^2+29 x+24$
• $y^2=71 x^6+80 x^5+72 x^4+38 x^3+54 x^2+109 x+77$
• $y^2=6 x^6+82 x^5+101 x^4+15 x^3+23 x^2+94 x+84$

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 4.0.784529424.1.

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.u_hv	$2$	(not in LMFDB)