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

• Label: 2.113.abk_vc
• 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:	$1 - 36 x + 548 x^{2} - 4068 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.133628584847$, $\pm0.215153007500$
Angle rank:	$2$ (numerical)
Number field:	4.0.10496.2
Galois group:	$D_{4}$
Jacobians:	$22$
Isomorphism classes:	22

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9214$	$160526308$	$2082421357150$	$26588663941374864$	$339464120671168237054$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$78$	$12570$	$1443222$	$163073254$	$18424752438$	$2081955858810$	$235260577506606$	$26584442038695934$	$3004041937374144846$	$339456738977598233850$

Jacobians and polarizations

This isogeny class contains the Jacobians of 22 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=79x^6+43x^5+47x^4+53x^3+57x^2+30x+89$
• $y^2=66x^6+2x^5+108x^4+31x^3+93x^2+67x+75$
• $y^2=34x^6+96x^5+96x^4+8x^3+57x^2+75x+92$
• $y^2=15x^6+37x^5+41x^4+10x^3+47x^2+104x+27$
• $y^2=87x^6+63x^5+72x^4+94x^3+75x^2+80x+20$
• $y^2=86x^6+102x^5+97x^4+26x^3+91x^2+46x+44$
• $y^2=111x^6+62x^5+77x^4+6x^3+64x^2+9x+96$
• $y^2=19x^6+33x^5+67x^4+65x^3+99x^2+34x+87$
• $y^2=98x^6+108x^5+15x^4+99x^3+74x^2+81x+62$
• $y^2=68x^6+81x^5+61x^4+58x^3+85x^2+89x+43$
• $y^2=70x^6+23x^5+33x^4+22x^3+36x^2+6x+96$
• $y^2=58x^6+68x^5+25x^4+36x^3+56x^2+57x+34$
• $y^2=55x^6+13x^5+5x^4+90x^3+17x^2+100x+86$
• $y^2=96x^6+31x^5+11x^4+47x^3+23x^2+54x+76$
• $y^2=19x^6+74x^5+57x^4+88x^3+79x^2+91x+53$
• $y^2=37x^6+29x^5+46x^4+106x^3+13x^2+33x+49$
• $y^2=108x^6+77x^5+26x^4+112x^3+30x^2+100x+21$
• $y^2=105x^6+92x^5+32x^4+18x^3+105x^2+86x+94$
• $y^2=46x^6+11x^5+86x^4+58x^3+37x^2+34x+82$
• $y^2=71x^6+29x^5+41x^3+89x^2+110x+91$
• $y^2=9x^6+83x^5+78x^4+27x^3+94x^2+21x+108$
• $y^2=45x^6+14x^5+71x^4+52x^3+10x^2+14$

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 4.0.10496.2.

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_vc	$2$	(not in LMFDB)