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

• Label: 2.107.abi_tc
• 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:	$1 - 34 x + 496 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.101476157912$, $\pm0.255918019012$
Angle rank:	$2$ (numerical)
Number field:	4.0.7316288.1
Galois group:	$D_{4}$
Jacobians:	$28$
Isomorphism classes:	28

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8274$	$129223332$	$1501188862698$	$17183980678841424$	$196717333640553251274$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$74$	$11286$	$1225418$	$131095766$	$14025674014$	$1500730900758$	$160578143107246$	$17181861756715294$	$1838459213460558554$	$196715135762162664966$

Jacobians and polarizations

This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=95x^6+3x^5+31x^4+31x^3+7x^2+76x+71$
• $y^2=100x^6+35x^5+48x^4+101x^3+74x^2+6x+95$
• $y^2=45x^6+74x^5+51x^4+52x^3+55x^2+55x+103$
• $y^2=106x^6+26x^5+29x^4+76x^3+91x^2+90x+65$
• $y^2=31x^6+x^5+88x^4+25x^3+49x^2+44x+71$
• $y^2=88x^6+18x^5+105x^4+88x^3+102x^2+79x+35$
• $y^2=60x^6+20x^5+103x^4+4x^3+44x^2+16x+95$
• $y^2=64x^6+40x^5+63x^4+87x^3+77x^2+14x+70$
• $y^2=67x^6+40x^5+21x^4+101x^3+14x^2+56x+97$
• $y^2=74x^6+24x^5+4x^4+50x^3+36x^2+83x+106$
• $y^2=63x^6+67x^5+89x^4+20x^3+6x^2+56x+45$
• $y^2=37x^6+85x^5+9x^4+19x^3+83x^2+88x+49$
• $y^2=80x^6+4x^5+38x^4+59x^3+19x^2+68x+53$
• $y^2=38x^6+29x^5+28x^4+82x^3+6x^2+49x+73$
• $y^2=91x^6+61x^5+76x^4+43x^3+103x^2+68x+82$
• $y^2=8x^6+99x^5+64x^4+19x^3+8x^2+102x+88$
• $y^2=74x^6+38x^5+45x^4+17x^3+67x^2+4x+47$
• $y^2=53x^6+18x^5+60x^4+43x^3+31x^2+81x+69$
• $y^2=96x^6+81x^5+9x^4+57x^3+60x^2+101x+26$
• $y^2=26x^6+71x^5+92x^4+15x^3+87x^2+96x+2$
• $y^2=89x^6+19x^5+106x^4+29x^3+78x^2+15x+1$
• $y^2=79x^6+95x^5+99x^4+10x^3+65x^2+40x+64$
• $y^2=18x^6+51x^5+101x^4+64x^3+x^2+6x$
• $y^2=98x^6+89x^5+102x^4+91x^3+77x^2+87x+50$
• $y^2=77x^6+85x^5+94x^4+42x^3+87x^2+102x+96$
• $y^2=95x^6+94x^5+102x^4+73x^3+83x^2+32x+58$
• $y^2=12x^6+88x^5+18x^4+90x^3+25x^2+16x+78$
• $y^2=66x^6+95x^5+65x^4+31x^3+29x^2+89x+90$

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 4.0.7316288.1.

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
2.107.bi_tc	$2$	(not in LMFDB)