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

• Label: 2.113.abl_vt
• Base field: $\F_{113}$
• Dimension: $2$
• $p$-rank: $1$
• Ordinary: no
• 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:	$1 - 37 x + 565 x^{2} - 4181 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0958952581556$, $\pm0.212472008282$
Angle rank:	$2$ (numerical)
Number field:	4.0.1164917.2
Galois group:	$D_{4}$
Jacobians:	$18$
Isomorphism classes:	18

This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

$p$-rank:	$1$
Slopes:	$[0, 1/2, 1/2, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9117$	$160030701$	$2081259110493$	$26586662263297461$	$339461322782047472592$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$77$	$12531$	$1442417$	$163060979$	$18424600582$	$2081954304891$	$235260564988561$	$26584441980251203$	$3004041937799280965$	$339456738994708910046$

Jacobians and polarizations

This isogeny class contains the Jacobians of 18 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=31x^6+32x^5+112x^4+48x^3+65x^2+32x+74$
• $y^2=63x^6+28x^5+44x^4+73x^3+87x^2+19x+58$
• $y^2=37x^6+94x^5+13x^4+42x^3+34x^2+26x+39$
• $y^2=31x^6+22x^5+107x^4+101x^3+100x^2+71x+26$
• $y^2=60x^6+71x^5+47x^4+17x^3+39x^2+98x+63$
• $y^2=78x^6+12x^5+4x^4+63x^3+55x^2+46x+8$
• $y^2=63x^6+63x^5+110x^4+73x^3+12x^2+54x+40$
• $y^2=50x^6+40x^5+103x^4+29x^3+51x^2+111x+68$
• $y^2=76x^6+110x^5+33x^4+44x^3+84x^2+42x+57$
• $y^2=16x^6+51x^5+16x^4+44x^3+82x^2+36x+25$
• $y^2=80x^6+66x^5+64x^4+83x^3+14x^2+100x+24$
• $y^2=96x^5+4x^4+82x^3+65x^2+39x+95$
• $y^2=63x^6+74x^5+111x^4+84x^3+77x^2+109x+33$
• $y^2=69x^6+37x^5+30x^4+70x^3+21x^2+42x+76$
• $y^2=36x^6+109x^5+75x^4+62x^3+81x^2+94x+89$
• $y^2=3x^6+2x^5+110x^4+81x^3+54x^2+107x+65$
• $y^2=74x^6+16x^5+32x^4+86x^3+52x^2+95x+35$
• $y^2=92x^6+3x^5+89x^4+109x^3+28x^2+91x+14$

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 4.0.1164917.2.

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.bl_vt	$2$	(not in LMFDB)