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

• Label: 2.113.ay_oe
• 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:	$1 - 24 x + 368 x^{2} - 2712 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.282664668060$, $\pm0.334099696073$
Angle rank:	$2$ (numerical)
Number field:	4.0.5918976.5
Galois group:	$D_{4}$
Jacobians:	$56$
Isomorphism classes:	56

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10402$	$165121348$	$2088504749506$	$26590307688869904$	$339455531413240657282$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$90$	$12930$	$1447434$	$163083334$	$18424286250$	$2081947200450$	$235260502549050$	$26584441875278974$	$3004041941927335962$	$339456739041390955650$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 56 curves (of which all are hyperelliptic):

• $y^2=20 x^6+46 x^5+111 x^4+86 x^3+31 x^2+78 x+87$
• $y^2=12 x^6+100 x^5+66 x^4+92 x^3+56 x^2+81 x+112$
• $y^2=22 x^6+33 x^5+80 x^4+23 x^3+62 x^2+27 x+91$
• $y^2=84 x^6+103 x^5+22 x^4+6 x^3+101 x^2+89 x+73$
• $y^2=111 x^6+17 x^4+5 x^3+45 x^2+69 x+21$
• $y^2=35 x^6+27 x^5+38 x^4+93 x^3+58 x^2+62 x+31$
• $y^2=21 x^6+5 x^5+42 x^4+112 x^3+105 x^2+89 x+55$
• $y^2=39 x^6+35 x^5+18 x^4+67 x^3+75 x^2+48 x+63$
• $y^2=62 x^6+58 x^5+7 x^4+89 x^3+62 x^2+34 x+93$
• $y^2=109 x^6+111 x^5+93 x^4+7 x^3+54 x^2+93 x+39$
• $y^2=107 x^6+46 x^5+42 x^4+64 x^3+78 x^2+4 x+48$
• $y^2=10 x^6+63 x^5+68 x^4+78 x^3+50 x^2+24 x+85$
• $y^2=105 x^6+40 x^5+76 x^4+24 x^3+56 x^2+3 x+11$
• $y^2=81 x^6+68 x^5+95 x^4+50 x^3+58 x^2+109 x+60$
• $y^2=28 x^6+78 x^5+33 x^4+61 x^3+25 x^2+52 x+52$
• $y^2=2 x^6+101 x^5+2 x^4+11 x^3+88 x^2+13 x+87$
• $y^2=85 x^6+75 x^5+29 x^4+97 x^3+102 x^2+85 x+47$
• $y^2=31 x^6+38 x^5+43 x^4+31 x^3+99 x^2+103 x+29$
• $y^2=3 x^6+3 x^5+53 x^4+16 x^3+102 x^2+42 x+86$
• $y^2=19 x^6+5 x^5+22 x^4+73 x^3+86 x^2+15 x+10$
• and

• $y^2=111 x^6+111 x^5+57 x^4+86 x^3+43 x^2+6 x+19$
• $y^2=25 x^6+66 x^5+90 x^4+76 x^3+75 x^2+109 x+90$
• $y^2=35 x^6+103 x^5+72 x^4+43 x^3+21 x^2+12 x+67$
• $y^2=95 x^6+62 x^5+97 x^4+103 x^3+87 x^2+111 x+34$
• $y^2=111 x^6+92 x^5+108 x^4+34 x^3+93 x^2+20 x+74$
• $y^2=22 x^6+73 x^5+90 x^4+18 x^3+103 x^2+111 x+81$
• $y^2=37 x^6+52 x^5+31 x^4+72 x^3+112 x^2+95 x+34$
• $y^2=80 x^6+29 x^5+7 x^4+98 x^3+109 x^2+4 x+85$
• $y^2=76 x^6+96 x^5+96 x^4+68 x^3+84 x^2+93 x+94$
• $y^2=98 x^6+90 x^5+79 x^4+91 x^3+85 x^2+16 x+80$
• $y^2=16 x^6+92 x^5+86 x^4+86 x^3+x^2+22 x+68$
• $y^2=102 x^6+39 x^5+8 x^4+24 x^3+50 x^2+10 x+3$
• $y^2=24 x^6+64 x^5+4 x^4+21 x^3+54 x^2+65 x+70$
• $y^2=7 x^6+90 x^5+9 x^4+15 x^3+88 x^2+73 x+8$
• $y^2=74 x^6+41 x^5+38 x^4+40 x^3+30 x^2+88 x+106$
• $y^2=105 x^6+3 x^5+65 x^4+77 x^3+13 x^2+43 x+17$
• $y^2=21 x^6+78 x^5+23 x^4+17 x^3+108 x^2+96 x+68$
• $y^2=65 x^6+74 x^5+53 x^4+77 x^3+47 x^2+26 x+107$
• $y^2=65 x^6+90 x^5+63 x^4+24 x^3+83 x^2+37 x+38$
• $y^2=41 x^6+111 x^5+79 x^4+7 x^3+58 x^2+80 x+79$
• $y^2=88 x^6+20 x^5+84 x^4+17 x^3+79 x^2+80 x+75$
• $y^2=96 x^6+95 x^5+76 x^4+52 x^3+27 x^2+67 x+35$
• $y^2=29 x^6+102 x^5+86 x^4+80 x^3+64 x^2+59 x+34$
• $y^2=39 x^6+13 x^5+99 x^4+78 x^3+64 x^2+111 x+38$
• $y^2=103 x^6+105 x^5+48 x^4+61 x^3+58 x^2+99 x+7$
• $y^2=66 x^6+63 x^5+100 x^4+69 x^3+32 x^2+25 x+89$
• $y^2=37 x^6+42 x^5+75 x^4+64 x^3+21 x^2+73 x+55$
• $y^2=66 x^6+58 x^5+3 x^4+78 x^3+64 x^2+60 x+68$
• $y^2=111 x^6+56 x^5+86 x^4+20 x^3+33 x^2+27 x+37$
• $y^2=56 x^6+91 x^5+88 x^4+105 x^3+98 x^2+43 x+46$
• $y^2=81 x^6+78 x^5+31 x^4+97 x^3+58 x^2+84 x+92$
• $y^2=70 x^6+88 x^5+73 x^4+108 x^3+64 x^2+10 x+76$
• $y^2=23 x^6+2 x^5+29 x^4+90 x^3+58 x^2+86 x+17$
• $y^2=28 x^6+40 x^5+94 x^4+69 x^3+30 x^2+93 x+61$
• $y^2=37 x^6+58 x^5+35 x^4+7 x^3+77 x^2+14 x+80$
• $y^2=100 x^6+69 x^5+43 x^4+63 x^3+56 x^2+107 x+12$

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 4.0.5918976.5.

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_oe	$2$	(not in LMFDB)