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

• Label: 2.113.abb_pl
• 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:	$1 - 27 x + 401 x^{2} - 3051 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.224396947475$, $\pm0.330260006094$
Angle rank:	$2$ (numerical)
Number field:	4.0.53505261.1
Galois group:	$D_{4}$
Jacobians:	$36$
Isomorphism classes:	36

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10093$	$164001157$	$2087216987989$	$26590612460204709$	$339459088987014178048$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$87$	$12843$	$1446543$	$163085203$	$18424479342$	$2081950210923$	$235260524182407$	$26584441808952931$	$3004041937977740079$	$339456738987092306718$

Jacobians and polarizations

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

• $y^2=39 x^6+54 x^5+15 x^4+28 x^3+15 x^2+39 x+15$
• $y^2=55 x^6+70 x^5+82 x^4+83 x^3+18 x^2+43 x+87$
• $y^2=83 x^6+10 x^5+74 x^4+57 x^3+33 x^2+102 x+27$
• $y^2=24 x^6+101 x^5+86 x^4+65 x^3+4 x^2+29 x+13$
• $y^2=69 x^6+68 x^5+66 x^4+85 x^3+58 x^2+63 x+26$
• $y^2=73 x^6+47 x^5+33 x^4+39 x^3+11 x^2+56 x+53$
• $y^2=34 x^6+59 x^5+77 x^4+30 x^3+7 x^2+112 x+12$
• $y^2=73 x^6+4 x^5+12 x^4+21 x^3+99 x^2+58 x+37$
• $y^2=55 x^6+82 x^5+27 x^4+34 x^3+3 x^2+3 x+45$
• $y^2=74 x^6+26 x^5+11 x^4+10 x^3+62 x^2+6 x+101$
• $y^2=94 x^6+51 x^5+48 x^4+87 x^3+16 x^2+107 x+20$
• $y^2=86 x^6+37 x^5+111 x^4+16 x^3+46 x^2+8 x+98$
• $y^2=66 x^6+32 x^5+90 x^4+11 x^3+77 x^2+80 x+54$
• $y^2=85 x^6+73 x^5+109 x^4+93 x^3+50 x^2+73 x+40$
• $y^2=104 x^6+69 x^5+62 x^4+78 x^3+91 x^2+99 x+78$
• $y^2=107 x^6+34 x^5+69 x^4+34 x^3+27 x^2+90 x+17$
• $y^2=65 x^6+18 x^5+11 x^4+15 x^3+83 x^2+15 x+1$
• $y^2=82 x^6+102 x^5+73 x^4+61 x^3+34 x^2+48 x+98$
• $y^2=47 x^6+49 x^5+107 x^4+105 x^3+107 x^2+23 x+88$
• $y^2=63 x^6+95 x^5+86 x^3+25 x^2+8 x+24$
• and

• $y^2=73 x^6+12 x^5+41 x^4+56 x^3+106 x^2+48 x+65$
• $y^2=8 x^6+67 x^5+89 x^4+108 x^3+33 x^2+101 x+14$
• $y^2=35 x^6+98 x^5+46 x^4+102 x^3+18 x^2+60 x+55$
• $y^2=44 x^6+17 x^5+73 x^4+39 x^3+9 x^2+12 x+61$
• $y^2=30 x^6+69 x^5+44 x^4+11 x^3+104 x^2+16 x+43$
• $y^2=45 x^6+110 x^5+27 x^4+50 x^3+69 x^2+17 x+95$
• $y^2=44 x^6+95 x^5+71 x^4+43 x^3+5 x^2+68 x+21$
• $y^2=58 x^6+61 x^5+53 x^4+92 x^3+19 x^2+48 x+10$
• $y^2=87 x^6+74 x^5+18 x^4+37 x^3+28 x^2+26 x+20$
• $y^2=22 x^6+9 x^5+9 x^4+90 x^3+11 x^2+93 x+108$
• $y^2=111 x^6+87 x^5+93 x^4+86 x^3+72 x^2+100 x+45$
• $y^2=86 x^6+26 x^5+12 x^4+24 x^3+98 x^2+31 x+37$
• $y^2=75 x^6+77 x^5+109 x^4+31 x^3+42 x^2+46 x+80$
• $y^2=65 x^6+16 x^5+35 x^4+95 x^3+37 x^2+103 x+111$
• $y^2=103 x^6+13 x^5+18 x^4+98 x^3+43 x^2+95 x+79$
• $y^2=12 x^6+81 x^5+15 x^4+60 x^3+53 x^2+31 x+38$

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 4.0.53505261.1.

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.bb_pl	$2$	(not in LMFDB)