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

• Label: 2.113.abj_tz
• 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:	$1 - 35 x + 519 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0338691187123$, $\pm0.273965054653$
Angle rank:	$2$ (numerical)
Number field:	4.0.3721925.1
Galois group:	$C_4$
Jacobians:	$10$
Isomorphism classes:	10

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9299$	$160677421$	$2081596484051$	$26584625768358821$	$339454417535489545264$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$79$	$12583$	$1442653$	$163048491$	$18424225794$	$2081948175487$	$235260495833113$	$26584441445435283$	$3004041935616499339$	$339456738999532863678$

Jacobians and polarizations

This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=16x^6+105x^5+12x^4+x^3+64x^2+76x+74$
• $y^2=89x^6+56x^5+57x^4+91x^3+67x^2+46x+11$
• $y^2=89x^6+14x^5+101x^4+7x^3+14x^2+87x+66$
• $y^2=60x^6+7x^5+41x^4+78x^3+111x^2+37x+40$
• $y^2=40x^6+10x^5+89x^4+104x^3+90x^2+8x+64$
• $y^2=81x^6+64x^5+39x^4+49x^3+64x^2+11x+79$
• $y^2=37x^6+83x^5+55x^4+112x^3+66x^2+66x+57$
• $y^2=5x^6+83x^5+12x^4+62x^3+13x^2+40x+65$
• $y^2=89x^6+63x^5+9x^4+45x^3+53x^2+15x+95$
• $y^2=64x^6+100x^5+19x^4+92x^3+40x^2+90x+65$

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 4.0.3721925.1.

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.bj_tz	$2$	(not in LMFDB)