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:	$18$
Isomorphism classes:	46

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 contains the Jacobians of 18 curves (of which all are hyperelliptic), and hence is principally polarizable:

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

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)