Abelian variety isogeny class 2.107.abi_tg over $\F_{107}$

• Label: 2.107.abi_tg
• Base field: $\F_{107}$
• 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:	$\F_{107}$
Dimension:	$2$
L-polynomial:	$1 - 34 x + 500 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.139535173173$, $\pm0.235768451684$
Angle rank:	$2$ (numerical)
Number field:	4.0.2164032.9
Galois group:	$D_{4}$
Jacobians:	$16$
Isomorphism classes:	16

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8278$	$129318916$	$1501690035022$	$17185360930933456$	$196719880140270695758$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$74$	$11294$	$1225826$	$131106294$	$14025855574$	$1500733137854$	$160578161391358$	$17181861797611678$	$1838459211787016810$	$196715135725885556654$

Jacobians and polarizations

This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=40x^6+70x^5+29x^4+62x^3+62x^2+100x+59$
• $y^2=87x^6+5x^5+102x^4+11x^3+11x^2+8x+48$
• $y^2=6x^6+104x^5+19x^4+9x^3+66x^2+2x+46$
• $y^2=80x^6+93x^5+53x^4+9x^3+83x^2+34x+78$
• $y^2=21x^6+2x^5+67x^4+57x^3+76x^2+22$
• $y^2=41x^6+25x^5+42x^4+32x^3+43x^2+19x+44$
• $y^2=7x^6+78x^5+70x^4+33x^3+71x^2+96x+93$
• $y^2=8x^6+46x^5+54x^4+17x^3+35x^2+87x+79$
• $y^2=78x^6+7x^5+95x^4+74x^3+85x^2+15x+94$
• $y^2=26x^6+87x^5+56x^4+4x^3+72x^2+67x+6$
• $y^2=48x^6+90x^5+25x^4+4x^3+45x^2+62x+98$
• $y^2=77x^6+66x^5+42x^4+74x^3+11x^2+85x+106$
• $y^2=98x^6+45x^5+89x^4+35x^3+20x^2+10x+31$
• $y^2=22x^6+60x^5+57x^4+80x^3+32x^2+35x+77$
• $y^2=90x^6+75x^5+86x^4+55x^3+66x^2+75x+54$
• $y^2=11x^6+31x^5+91x^4+26x^3+59x^2+99x+9$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{107}$.

Endomorphism algebra over $\F_{107}$

The endomorphism algebra of this simple isogeny class is 4.0.2164032.9.

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
2.107.bi_tg	$2$	(not in LMFDB)