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

• Label: 2.113.abe_qx
• 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:	$1 - 30 x + 439 x^{2} - 3390 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.165098416172$, $\pm0.317438811485$
Angle rank:	$2$ (numerical)
Number field:	4.0.5101200.1
Galois group:	$D_{4}$
Jacobians:	$72$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9789$	$162781281$	$2085330935376$	$26589208990169241$	$339459654665727868389$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$84$	$12748$	$1445238$	$163076596$	$18424510044$	$2081951879902$	$235260551615628$	$26584442143485988$	$3004041941260158294$	$339456739006847558428$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 72 curves (of which all are hyperelliptic):

• $y^2=56 x^6+47 x^5+72 x^4+34 x^3+7 x^2+12 x+41$
• $y^2=3 x^6+53 x^5+72 x^4+58 x^3+60 x^2+43 x+51$
• $y^2=86 x^6+71 x^5+18 x^4+102 x^3+41 x^2+22 x+77$
• $y^2=47 x^6+33 x^5+30 x^4+44 x^3+111 x^2+46 x+38$
• $y^2=79 x^6+37 x^5+97 x^4+95 x^3+28 x^2+69 x+74$
• $y^2=9 x^6+58 x^5+3 x^4+8 x^3+100 x^2+51 x+63$
• $y^2=58 x^6+57 x^5+57 x^4+90 x^3+27 x^2+93 x+59$
• $y^2=101 x^6+47 x^5+27 x^4+96 x^3+100 x^2+49 x+94$
• $y^2=74 x^6+97 x^5+23 x^4+59 x^3+14 x^2+44 x+62$
• $y^2=103 x^6+82 x^5+106 x^4+85 x^3+91 x^2+14 x+11$
• $y^2=80 x^6+59 x^5+62 x^4+30 x^3+52 x^2+36 x+84$
• $y^2=44 x^6+63 x^5+86 x^4+37 x^3+102 x^2+34 x+20$
• $y^2=26 x^6+78 x^5+100 x^4+24 x^3+59 x+97$
• $y^2=18 x^6+75 x^5+9 x^4+2 x^3+60 x^2+52 x+45$
• $y^2=67 x^6+111 x^5+62 x^4+x^3+14 x^2+40 x+33$
• $y^2=18 x^6+87 x^5+38 x^4+6 x^3+63 x^2+58 x+106$
• $y^2=62 x^6+29 x^5+11 x^4+83 x^3+95 x^2+35 x+100$
• $y^2=40 x^6+84 x^5+22 x^4+51 x^3+68 x^2+44 x+40$
• $y^2=106 x^6+3 x^5+36 x^4+71 x^3+103 x^2+70 x+13$
• $y^2=110 x^6+110 x^5+20 x^4+34 x^3+47 x^2+8 x+73$
• and

• $y^2=98 x^6+17 x^5+54 x^4+81 x^3+29 x^2+57 x+70$
• $y^2=47 x^6+28 x^5+110 x^4+110 x^3+35 x^2+100 x+79$
• $y^2=66 x^6+102 x^5+62 x^4+33 x^3+98 x^2+4 x+64$
• $y^2=90 x^6+70 x^5+89 x^4+38 x^3+98 x^2+8 x+40$
• $y^2=4 x^6+28 x^5+93 x^4+79 x^3+89 x^2+105 x+65$
• $y^2=57 x^6+57 x^5+41 x^4+2 x^3+25 x^2+29 x+21$
• $y^2=87 x^6+106 x^5+26 x^4+39 x^3+41 x^2+48 x+103$
• $y^2=107 x^6+38 x^5+8 x^4+97 x^3+85 x^2+93 x+83$
• $y^2=55 x^6+58 x^5+61 x^4+90 x^3+7 x^2+66 x+96$
• $y^2=24 x^6+99 x^5+70 x^4+86 x^3+48 x^2+71 x+25$
• $y^2=102 x^6+62 x^5+44 x^4+72 x^3+81 x^2+62 x+111$
• $y^2=94 x^6+39 x^5+108 x^4+4 x^3+58 x^2+16 x+95$
• $y^2=63 x^6+46 x^5+96 x^4+76 x^3+103 x+35$
• $y^2=54 x^6+110 x^5+89 x^4+68 x^3+32 x^2+96 x+60$
• $y^2=69 x^6+27 x^5+40 x^4+103 x^3+27 x^2+42 x+33$
• $y^2=84 x^6+82 x^5+46 x^4+74 x^3+78 x^2+59 x+49$
• $y^2=71 x^6+43 x^5+69 x^4+50 x^3+74 x^2+71 x+93$
• $y^2=13 x^6+27 x^4+66 x^3+101 x^2+48 x+38$
• $y^2=42 x^6+35 x^5+7 x^4+76 x^3+48 x^2+77 x+81$
• $y^2=70 x^6+14 x^5+95 x^4+57 x^3+95 x^2+11 x+65$
• $y^2=84 x^6+66 x^5+9 x^4+32 x^3+90 x^2+99 x+24$
• $y^2=6 x^6+30 x^5+101 x^4+31 x^3+29 x^2+78 x+77$
• $y^2=63 x^6+73 x^5+61 x^4+35 x^3+31 x^2+31 x+18$
• $y^2=10 x^6+112 x^5+107 x^4+100 x^3+71 x^2+78 x+14$
• $y^2=58 x^6+77 x^5+105 x^4+20 x^3+11 x^2+61 x+80$
• $y^2=69 x^6+2 x^5+17 x^4+57 x^3+79 x^2+2 x+87$
• $y^2=112 x^6+51 x^5+66 x^4+3 x^3+96 x^2+109 x+89$
• $y^2=20 x^6+68 x^5+60 x^4+77 x^3+27 x^2+89 x+103$
• $y^2=31 x^6+71 x^5+46 x^4+35 x^3+109 x^2+43 x+44$
• $y^2=111 x^6+86 x^5+30 x^4+11 x^3+5 x^2+43 x+75$
• $y^2=6 x^6+16 x^5+107 x^4+55 x^3+75 x^2+98 x+73$
• $y^2=36 x^6+66 x^5+93 x^4+94 x^3+x^2+47 x+86$
• $y^2=43 x^6+101 x^5+42 x^4+11 x^3+53 x^2+28 x+96$
• $y^2=79 x^6+31 x^5+50 x^4+31 x^3+83 x^2+26 x+81$
• $y^2=21 x^6+107 x^5+44 x^4+6 x^3+32 x^2+8 x+5$
• $y^2=47 x^6+20 x^5+52 x^4+104 x^3+49 x^2+110 x+103$
• $y^2=103 x^6+43 x^5+91 x^4+59 x^3+71 x^2+97 x+26$
• $y^2=63 x^6+15 x^5+25 x^4+65 x^3+12 x^2+91 x+35$
• $y^2=37 x^6+19 x^5+60 x^4+19 x^3+52 x^2+86 x+101$
• $y^2=5 x^6+108 x^5+33 x^4+64 x^3+20 x^2+11 x+44$
• $y^2=86 x^6+90 x^5+88 x^4+36 x^3+77 x^2+14 x+76$
• $y^2=78 x^6+35 x^5+88 x^4+44 x^3+71 x^2+66 x+18$
• $y^2=43 x^6+82 x^5+94 x^4+44 x^3+45 x^2+39 x+37$
• $y^2=70 x^6+81 x^5+104 x^4+84 x^3+94 x^2+82 x+101$
• $y^2=4 x^6+33 x^5+79 x^4+81 x^3+92 x^2+37 x+111$
• $y^2=20 x^6+80 x^5+79 x^4+35 x^3+29 x^2+59 x+75$
• $y^2=73 x^6+73 x^5+75 x^4+28 x^3+10 x^2+65 x+88$
• $y^2=109 x^6+32 x^5+53 x^4+6 x^3+5 x^2+28 x+5$
• $y^2=106 x^6+69 x^5+x^4+22 x^3+62 x^2+x+39$
• $y^2=25 x^6+102 x^5+39 x^4+42 x^3+29 x^2+14 x+59$
• $y^2=59 x^6+50 x^5+22 x^4+18 x^3+50 x^2+4 x+32$
• $y^2=47 x^6+39 x^5+x^4+14 x^3+31 x^2+13 x+91$

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 4.0.5101200.1.

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.be_qx	$2$	(not in LMFDB)