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

• Label: 2.113.abi_tg
• 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:	$1 - 34 x + 500 x^{2} - 3842 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0608513799594$, $\pm0.288168650894$
Angle rank:	$2$ (numerical)
Number field:	4.0.16430400.1
Galois group:	$D_{4}$
Jacobians:	$12$
Isomorphism classes:	24

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9394$	$161069524$	$2082195515554$	$26585131201888336$	$339454777675268908114$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$80$	$12614$	$1443068$	$163051590$	$18424245340$	$2081948664278$	$235260510341776$	$26584441728343294$	$3004041939505213904$	$339456739038874804214$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=66x^6+92x^5+91x^4+71x^3+43x^2+65x+87$
• $y^2=54x^6+55x^5+75x^4+90x^3+88x^2+42x+107$
• $y^2=18x^6+101x^5+33x^4+75x^3+x^2+29x+99$
• $y^2=107x^6+8x^5+53x^4+30x^3+105x^2+45x+83$
• $y^2=97x^6+29x^5+19x^4+22x^3+107x^2+2x+1$
• $y^2=38x^6+97x^5+52x^4+54x^3+76x^2+52x$
• $y^2=97x^6+83x^5+86x^4+76x^3+65x^2+20x+70$
• $y^2=112x^6+40x^5+39x^4+33x^3+112x^2+69x+38$
• $y^2=88x^6+29x^5+36x^4+47x^3+18x^2+47x+99$
• $y^2=70x^6+46x^5+104x^4+30x^3+8x^2+46x+84$
• $y^2=86x^6+69x^5+89x^4+25x^3+46x^2+90x+43$
• $y^2=33x^6+62x^5+87x^4+68x^3+39x^2+6x+23$

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 4.0.16430400.1.

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.bi_tg	$2$	(not in LMFDB)