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

• Label: 2.113.abj_ua
• Base field: $\F_{113}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{113}$
Dimension:	$2$
L-polynomial:	$( 1 - 21 x + 113 x^{2} )( 1 - 14 x + 113 x^{2} )$
	$1 - 35 x + 520 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0498602789898$, $\pm0.271189304635$
Angle rank:	$2$ (numerical)
Jacobians:	$30$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9300$	$160704000$	$2081748344400$	$26585085945600000$	$339455381592115816500$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$79$	$12585$	$1442758$	$163051313$	$18424278119$	$2081948928030$	$235260504909383$	$26584441546270753$	$3004041936786461734$	$339456739014818158425$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 30 curves (of which all are hyperelliptic):

• $y^2=76 x^6+11 x^5+24 x^4+5 x^3+35 x^2+62 x+95$
• $y^2=82 x^6+20 x^5+57 x^4+30 x^3+45 x^2+9 x+61$
• $y^2=47 x^6+85 x^5+46 x^4+31 x^3+90 x^2+102 x+75$
• $y^2=23 x^6+22 x^5+3 x^4+40 x^3+6 x^2+43 x+99$
• $y^2=99 x^6+91 x^5+44 x^4+8 x^3+2 x^2+55 x+63$
• $y^2=23 x^6+64 x^5+7 x^4+57 x^3+62 x^2+96 x+35$
• $y^2=71 x^6+95 x^5+23 x^4+17 x^3+37 x^2+101 x+78$
• $y^2=25 x^6+112 x^5+4 x^4+27 x^3+17 x^2+89 x+41$
• $y^2=38 x^6+102 x^5+68 x^4+102 x^3+41 x^2+40 x+19$
• $y^2=76 x^6+104 x^5+4 x^4+98 x^3+25 x^2+37 x+14$
• $y^2=98 x^6+52 x^5+15 x^4+19 x^3+97 x^2+103 x+32$
• $y^2=58 x^6+103 x^5+110 x^4+41 x^3+94 x^2+81 x+56$
• $y^2=25 x^6+104 x^5+26 x^3+53 x^2+35 x+41$
• $y^2=29 x^6+23 x^5+108 x^4+6 x^3+6 x^2+10 x+29$
• $y^2=56 x^6+96 x^5+70 x^4+65 x^3+93 x^2+12 x+28$
• $y^2=95 x^6+91 x^5+83 x^4+66 x^3+17 x^2+29 x+45$
• $y^2=23 x^6+60 x^5+71 x^4+88 x^3+11 x^2+55 x+65$
• $y^2=21 x^6+86 x^5+74 x^3+9 x^2+6 x+20$
• $y^2=72 x^6+22 x^5+38 x^4+83 x^3+16 x^2+85 x+58$
• $y^2=24 x^6+56 x^5+25 x^4+72 x^3+36 x^2+38 x+91$
• $y^2=87 x^6+60 x^5+54 x^4+90 x^3+30 x^2+54 x+76$
• $y^2=51 x^6+58 x^5+106 x^4+100 x^3+87 x^2+12 x+1$
• $y^2=80 x^6+68 x^5+32 x^4+28 x^3+93 x^2+50 x+111$
• $y^2=103 x^6+5 x^5+90 x^4+58 x^3+44 x^2+107 x+23$
• $y^2=8 x^6+26 x^5+72 x^4+16 x^3+110 x^2+16 x+57$
• $y^2=97 x^6+107 x^5+70 x^4+59 x^3+50 x^2+76 x+76$
• $y^2=40 x^6+8 x^5+32 x^4+32 x^3+58 x^2+103 x+47$
• $y^2=72 x^6+81 x^5+101 x^4+12 x^3+10 x^2+83 x+45$
• $y^2=101 x^6+92 x^5+36 x^4+17 x^3+58 x^2+64 x+49$
• $y^2=3 x^6+27 x^5+8 x^4+50 x^3+103 x^2+52 x+17$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{113}$.

Endomorphism algebra over $\F_{113}$

The isogeny class factors as 1.113.av $\times$ 1.113.ao and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.113.av : \(\Q(\sqrt{-11}) \).
• 1.113.ao : \(\Q(\sqrt{-1}) \).

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.113.ah_acq	$2$	(not in LMFDB)
2.113.h_acq	$2$	(not in LMFDB)
2.113.bj_ua	$2$	(not in LMFDB)