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

• Label: 2.113.abk_uy
• 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:	$1 - 36 x + 544 x^{2} - 4068 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0881917305060$, $\pm0.238851186738$
Angle rank:	$2$ (numerical)
Number field:	4.0.4094208.2
Galois group:	$D_{4}$
Jacobians:	$32$
Isomorphism classes:	32

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9210$	$160419780$	$2081796358410$	$26586707020938000$	$339459915449879647050$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$78$	$12562$	$1442790$	$163061254$	$18424524198$	$2081952618514$	$235260543321294$	$26584441811918206$	$3004041937657675950$	$339456739013920454482$

Jacobians and polarizations

This isogeny class contains the Jacobians of 32 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=49x^6+35x^5+71x^4+92x^3+110x^2+57x+93$
• $y^2=27x^6+70x^5+18x^4+73x^3+73x^2+50x+93$
• $y^2=73x^6+38x^5+38x^4+105x^3+64x^2+39x+19$
• $y^2=13x^6+61x^5+51x^4+80x^3+87x^2+39x+63$
• $y^2=72x^6+91x^5+98x^4+21x^3+71x^2+58x+81$
• $y^2=47x^6+13x^5+17x^4+7x^3+84x^2+10x+42$
• $y^2=67x^6+109x^5+101x^4+15x^3+76x^2+22x+41$
• $y^2=40x^6+87x^5+94x^4+49x^3+45x^2+111x+47$
• $y^2=33x^6+22x^5+26x^4+104x^3+105x^2+62x+35$
• $y^2=101x^6+56x^5+61x^4+106x^3+59x^2+32x+61$
• $y^2=89x^6+28x^5+32x^4+83x^3+12x^2+48x+65$
• $y^2=3x^6+81x^5+99x^4+31x^3+35x^2+75x+105$
• $y^2=92x^6+104x^5+27x^4+78x^3+12x^2+8x+92$
• $y^2=75x^6+35x^5+64x^4+58x^3+10x^2+108x+25$
• $y^2=19x^6+26x^5+12x^4+45x^3+74x+2$
• $y^2=21x^6+72x^4+45x^3+87x^2+29x+108$
• $y^2=96x^6+71x^5+101x^3+81x^2+12x+50$
• $y^2=21x^6+24x^5+x^4+36x^3+19x^2+103x+88$
• $y^2=32x^6+41x^5+69x^4+18x^3+73x^2+13x+104$
• $y^2=17x^6+23x^5+64x^4+35x^3+107x^2+70x+112$
• and

• $y^2=17x^6+92x^5+46x^4+56x^3+72x^2+79x+21$
• $y^2=40x^6+55x^5+49x^4+26x^3+65x^2+24x+13$
• $y^2=79x^6+47x^5+39x^4+49x^3+9x^2+90x+112$
• $y^2=34x^6+81x^5+31x^4+57x^3+99x^2+62x+48$
• $y^2=19x^6+7x^5+29x^4+27x^3+38x^2+100x+54$
• $y^2=87x^6+42x^5+78x^4+56x^3+3x^2+38x+14$
• $y^2=x^6+45x^5+33x^4+81x^3+86x^2+65x+84$
• $y^2=20x^6+12x^5+105x^4+3x^3+41x^2+89x+110$
• $y^2=73x^6+68x^5+85x^4+67x^3+48x^2+8x+93$
• $y^2=58x^6+43x^5+70x^4+41x^3+39x^2+87x+90$
• $y^2=57x^6+70x^5+19x^4+95x^3+65x^2+102x+61$
• $y^2=22x^6+63x^5+87x^4+67x^3+109x^2+95x+93$

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 4.0.4094208.2.

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.bk_uy	$2$	(not in LMFDB)