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

• Label: 2.113.abb_ol
• 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:	$1 - 27 x + 375 x^{2} - 3051 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.138962790671$, $\pm0.381491622538$
Angle rank:	$2$ (numerical)
Number field:	4.0.560617477.1
Galois group:	$D_{4}$
Jacobians:	$34$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10067$	$163316941$	$2084173919363$	$26584829809461541$	$339454820792392732592$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$87$	$12791$	$1444437$	$163049739$	$18424247682$	$2081952477551$	$235260594260961$	$26584442557049683$	$3004041941150020515$	$339456738973951795646$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 34 curves (of which all are hyperelliptic):

• $y^2=91 x^6+67 x^5+84 x^4+87 x^3+25 x^2+97 x+106$
• $y^2=110 x^6+61 x^5+33 x^4+47 x^3+40 x^2+62 x+7$
• $y^2=104 x^6+96 x^5+105 x^4+33 x^3+72 x^2+23 x+4$
• $y^2=39 x^6+48 x^5+60 x^4+43 x^3+112 x^2+12 x+26$
• $y^2=66 x^6+23 x^5+105 x^4+88 x^3+24 x^2+93 x+75$
• $y^2=110 x^6+107 x^5+108 x^4+94 x^3+37 x^2+15 x+40$
• $y^2=87 x^6+2 x^5+73 x^4+25 x^3+94 x^2+75$
• $y^2=47 x^6+78 x^5+6 x^4+38 x^2+12 x+42$
• $y^2=98 x^6+108 x^5+7 x^4+27 x^3+34 x^2+44 x+11$
• $y^2=112 x^5+101 x^4+104 x^3+97 x^2+48 x+79$
• $y^2=73 x^6+59 x^5+42 x^4+27 x^3+102 x^2+43 x+98$
• $y^2=42 x^6+68 x^5+112 x^4+45 x^3+51 x^2+94 x+1$
• $y^2=27 x^6+89 x^5+59 x^4+60 x^3+33 x^2+51 x+44$
• $y^2=44 x^6+106 x^5+80 x^4+106 x^3+82 x^2+65 x+108$
• $y^2=4 x^6+101 x^5+84 x^4+11 x^3+40 x^2+79 x+74$
• $y^2=9 x^6+31 x^5+43 x^4+54 x^3+88 x^2+54 x+49$
• $y^2=74 x^6+57 x^5+52 x^4+7 x^3+80 x^2+29 x+63$
• $y^2=88 x^6+61 x^5+30 x^4+109 x^3+21 x+59$
• $y^2=81 x^6+3 x^5+9 x^4+41 x^3+81 x^2+79 x+28$
• $y^2=8 x^6+45 x^5+31 x^4+x^3+34 x^2+2 x+50$
• and

• $y^2=2 x^6+32 x^5+103 x^4+50 x^3+70 x^2+88 x+79$
• $y^2=33 x^6+7 x^5+85 x^4+31 x^3+23 x^2+106 x+103$
• $y^2=21 x^6+63 x^5+2 x^4+58 x^3+39 x^2+9 x+111$
• $y^2=79 x^6+88 x^5+65 x^4+17 x^3+79 x^2+49 x+11$
• $y^2=13 x^6+51 x^5+15 x^4+99 x^3+45 x^2+45 x+29$
• $y^2=85 x^6+63 x^5+106 x^4+88 x^3+62 x^2+89 x+58$
• $y^2=64 x^6+7 x^5+85 x^4+74 x^3+48 x^2+40 x+34$
• $y^2=104 x^6+98 x^5+77 x^4+95 x^3+72 x^2+24 x+33$
• $y^2=90 x^6+106 x^5+101 x^4+108 x^3+14 x^2+85 x+23$
• $y^2=97 x^6+23 x^5+89 x^4+52 x^3+18 x^2+89 x+38$
• $y^2=26 x^6+17 x^5+28 x^4+72 x^3+66 x^2+4 x+11$
• $y^2=89 x^6+81 x^5+22 x^4+86 x^3+41 x^2+105 x+4$
• $y^2=58 x^6+25 x^5+17 x^4+73 x^3+48 x^2+83 x+66$
• $y^2=84 x^5+72 x^4+78 x^3+106 x^2+x+101$

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 4.0.560617477.1.

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_ol	$2$	(not in LMFDB)