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

• Label: 2.113.abl_vv
• 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:	$1 - 37 x + 567 x^{2} - 4181 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.125932323751$, $\pm0.195315764367$
Angle rank:	$2$ (numerical)
Number field:	4.0.251525.1
Galois group:	$D_{4}$
Jacobians:	$11$
Isomorphism classes:	11

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9119$	$160084045$	$2081580351191$	$26587709893247525$	$339463708769380319344$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$77$	$12535$	$1442639$	$163067403$	$18424730082$	$2081956303855$	$235260589050179$	$26584442191425363$	$3004041938639982977$	$339456738981053615550$

Jacobians and polarizations

This isogeny class contains the Jacobians of 11 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=22x^6+41x^5+47x^4+71x^3+19x^2+5x+10$
• $y^2=83x^6+45x^5+12x^4+94x^3+22x^2+20x+2$
• $y^2=108x^6+103x^5+93x^4+63x^3+44x^2+97x+59$
• $y^2=107x^6+22x^5+45x^4+72x^3+86x^2+95x+73$
• $y^2=20x^6+24x^5+2x^4+99x^3+101x+52$
• $y^2=36x^6+62x^5+36x^4+110x^3+12x^2+106x+40$
• $y^2=50x^6+29x^5+107x^4+65x^3+16x+70$
• $y^2=58x^6+31x^5+40x^4+70x^3+88x^2+93x+43$
• $y^2=94x^6+67x^5+101x^4+107x^3+29x^2+102x+41$
• $y^2=110x^6+103x^5+89x^4+105x^3+32x^2+71x+109$
• $y^2=59x^6+89x^5+61x^4+39x^3+89x^2+24x+48$

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 4.0.251525.1.

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.bl_vv	$2$	(not in LMFDB)