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

• Label: 2.113.abe_qg
• 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:	$1 - 30 x + 422 x^{2} - 3390 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0916467577024$, $\pm0.350623691245$
Angle rank:	$2$ (numerical)
Number field:	4.0.11020464.2
Galois group:	$D_{4}$
Jacobians:	$48$
Isomorphism classes:	64

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9772$	$162332464$	$2083119686284$	$26584003251622656$	$339452513410871662732$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$84$	$12714$	$1443708$	$163044670$	$18424122444$	$2081949469098$	$235260556856388$	$26584442413931134$	$3004041943999254564$	$339456739027087495914$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 48 curves (of which all are hyperelliptic):

• $y^2=33 x^6+7 x^5+49 x^4+53 x^3+12 x^2+24 x+38$
• $y^2=99 x^6+111 x^5+85 x^4+15 x^3+x^2+35 x+51$
• $y^2=107 x^6+20 x^5+72 x^4+17 x^3+93 x^2+85 x+97$
• $y^2=108 x^6+78 x^5+3 x^4+46 x^3+110 x^2+100 x+5$
• $y^2=90 x^6+2 x^5+44 x^4+105 x^3+77 x^2+30 x+33$
• $y^2=46 x^6+23 x^5+12 x^4+108 x^3+51 x^2+98 x+87$
• $y^2=107 x^6+9 x^5+17 x^4+106 x^3+17 x^2+78 x+15$
• $y^2=110 x^6+19 x^5+96 x^4+52 x^3+44 x^2+9 x+9$
• $y^2=53 x^6+60 x^5+3 x^4+38 x^3+17 x^2+105 x+71$
• $y^2=86 x^6+82 x^5+14 x^4+3 x^3+111 x+107$
• $y^2=43 x^6+80 x^5+52 x^4+97 x^3+18 x^2+5$
• $y^2=25 x^6+4 x^5+21 x^4+33 x^3+106 x^2+66 x+95$
• $y^2=50 x^6+64 x^5+54 x^4+74 x^3+3 x^2+48 x+11$
• $y^2=58 x^6+41 x^5+55 x^4+24 x^3+44 x^2+41 x+54$
• $y^2=64 x^5+39 x^4+58 x^3+110 x^2+112 x+71$
• $y^2=54 x^6+86 x^5+96 x^4+11 x^3+5 x^2+65 x+42$
• $y^2=44 x^6+94 x^5+17 x^4+80 x^3+61 x^2+65 x+80$
• $y^2=12 x^6+53 x^5+77 x^4+25 x^3+16 x^2+79 x+28$
• $y^2=65 x^6+19 x^5+3 x^4+33 x^3+90 x^2+74 x+95$
• $y^2=76 x^6+62 x^5+44 x^4+15 x^3+31 x^2+46 x+36$
• and

• $y^2=103 x^6+107 x^5+103 x^4+95 x^3+91 x^2+7 x+94$
• $y^2=10 x^6+108 x^5+52 x^4+42 x^3+4 x^2+20 x+80$
• $y^2=90 x^6+74 x^5+80 x^4+56 x^3+62 x^2+109 x+62$
• $y^2=42 x^6+51 x^5+34 x^4+44 x^3+55 x^2+18 x+32$
• $y^2=95 x^6+77 x^5+105 x^4+108 x^3+64 x^2+56 x+12$
• $y^2=91 x^6+80 x^5+83 x^4+36 x^3+71 x^2+10 x+33$
• $y^2=39 x^6+91 x^5+83 x^4+7 x^3+75 x^2+73 x+71$
• $y^2=33 x^6+53 x^5+32 x^4+47 x^3+47 x^2+53 x+87$
• $y^2=45 x^6+38 x^5+92 x^4+32 x^3+45 x^2+67 x+31$
• $y^2=5 x^6+20 x^5+18 x^4+13 x^3+88 x^2+45 x+112$
• $y^2=25 x^6+20 x^5+7 x^4+70 x^3+61 x^2+72 x+61$
• $y^2=74 x^6+3 x^5+8 x^4+74 x^3+41 x^2+100 x+49$
• $y^2=18 x^6+89 x^5+14 x^4+79 x^3+20 x^2+92 x+30$
• $y^2=17 x^6+55 x^5+64 x^4+13 x^3+75 x^2+101 x+38$
• $y^2=57 x^6+105 x^5+37 x^4+100 x^3+39 x^2+69 x+27$
• $y^2=72 x^6+28 x^5+72 x^4+56 x^3+87 x^2+83 x+86$
• $y^2=86 x^6+110 x^5+36 x^4+46 x^3+52 x+28$
• $y^2=80 x^6+77 x^5+11 x^4+6 x^3+70 x^2+6 x+71$
• $y^2=69 x^6+25 x^5+11 x^4+99 x^3+72 x^2+93 x+24$
• $y^2=32 x^6+94 x^5+54 x^4+90 x^3+62 x^2+33 x+46$
• $y^2=95 x^6+93 x^5+66 x^4+100 x^3+70 x^2+99 x+94$
• $y^2=48 x^6+77 x^5+48 x^4+66 x^3+74 x^2+80 x+73$
• $y^2=96 x^6+14 x^5+58 x^3+38 x^2+26 x+10$
• $y^2=59 x^6+109 x^5+79 x^4+79 x^3+31 x^2+93 x+21$
• $y^2=46 x^6+18 x^5+14 x^4+82 x^3+64 x^2+69 x+48$
• $y^2=81 x^6+2 x^5+8 x^4+78 x^3+84 x^2+80 x+24$
• $y^2=42 x^6+26 x^5+50 x^4+23 x^3+49 x^2+44 x+59$
• $y^2=23 x^6+45 x^5+98 x^4+17 x^3+93 x^2+6 x+91$

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 4.0.11020464.2.

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_qg	$2$	(not in LMFDB)