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

• Label: 2.113.abj_uk
• 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:	$( 1 - 19 x + 113 x^{2} )( 1 - 16 x + 113 x^{2} )$
	$1 - 35 x + 530 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.148111132014$, $\pm0.228810695365$
Angle rank:	$2$ (numerical)
Jacobians:	$18$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9310$	$160969900$	$2083267120480$	$26589651961600000$	$339464667533711745550$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$79$	$12605$	$1443808$	$163079313$	$18424782119$	$2081955585890$	$235260568883783$	$26584441920742753$	$3004041936314164384$	$339456738971650064525$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 18 curves (of which all are hyperelliptic):

• $y^2=10 x^6+29 x^5+66 x^4+32 x^3+6 x^2+81 x+3$
• $y^2=74 x^6+100 x^5+21 x^4+65 x^3+58 x^2+58 x+82$
• $y^2=55 x^6+63 x^5+45 x^4+14 x^3+12 x^2+106 x+47$
• $y^2=87 x^6+48 x^5+87 x^4+16 x^3+80 x^2+19 x+89$
• $y^2=44 x^6+19 x^5+66 x^4+33 x^3+112 x^2+37 x+55$
• $y^2=39 x^6+15 x^5+39 x^4+89 x^3+55 x^2+49 x+73$
• $y^2=48 x^6+68 x^5+34 x^4+5 x^3+6 x^2+73 x+20$
• $y^2=111 x^6+24 x^5+94 x^4+70 x^3+35 x^2+55 x+40$
• $y^2=62 x^6+6 x^5+103 x^4+50 x^3+42 x^2+55 x+34$
• $y^2=15 x^6+15 x^5+59 x^4+17 x^3+66 x^2+104 x+48$
• $y^2=52 x^6+53 x^5+82 x^4+49 x^3+48 x^2+31 x+58$
• $y^2=37 x^6+95 x^5+35 x^4+19 x^3+103 x^2+10 x+18$
• $y^2=26 x^6+72 x^5+86 x^4+93 x^3+112 x^2+16 x+41$
• $y^2=5 x^6+45 x^5+26 x^4+30 x^3+23 x+27$
• $y^2=23 x^6+103 x^5+17 x^4+5 x^3+17 x^2+111 x+6$
• $y^2=75 x^6+30 x^5+29 x^4+53 x^3+9 x^2+12 x+69$
• $y^2=39 x^6+107 x^5+112 x^4+26 x^3+93 x^2+2 x+111$
• $y^2=29 x^6+52 x^5+85 x^4+12 x^3+63 x+93$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{113}$

The isogeny class factors as 1.113.at $\times$ 1.113.aq 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.at : \(\Q(\sqrt{-91}) \).
• 1.113.aq : \(\Q(\sqrt{-1}) \).

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.ad_ada	$2$	(not in LMFDB)
2.113.d_ada	$2$	(not in LMFDB)
2.113.bj_uk	$2$	(not in LMFDB)