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

• Label: 2.107.ac_afc
• 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:	$1 - 2 x - 132 x^{2} - 214 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.102347107508$, $\pm0.824658098163$
Angle rank:	$2$ (numerical)
Number field:	4.0.9655838528.1
Galois group:	$D_{4}$
Jacobians:	$128$
Isomorphism classes:	128

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$11102$	$128050468$	$1498966516502$	$17182793687228624$	$196712182233607083862$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$106$	$11182$	$1223602$	$131086710$	$14025306726$	$1500733628686$	$160578144435262$	$17181862097992350$	$1838459215707636202$	$196715135736884363262$

Jacobians and polarizations

This isogeny class contains the Jacobians of 128 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=78x^6+20x^5+104x^4+24x^3+52x^2+44x+30$
• $y^2=2x^6+7x^5+72x^4+51x^3+10x^2+80x+84$
• $y^2=80x^6+89x^5+37x^4+x^3+20x^2+7x+17$
• $y^2=32x^6+20x^5+6x^4+52x^3+14x^2+67x+15$
• $y^2=17x^6+84x^5+2x^4+3x^3+37x^2+30x+95$
• $y^2=54x^6+74x^5+103x^4+91x^3+23x^2+58x+34$
• $y^2=65x^6+59x^5+26x^4+104x^3+25x^2+41x+15$
• $y^2=54x^6+66x^5+38x^4+10x^3+31x^2+40x+60$
• $y^2=94x^6+24x^5+44x^4+86x^3+27x^2+7x+100$
• $y^2=63x^6+17x^5+67x^4+6x^3+52x^2+43x+4$
• $y^2=23x^6+77x^5+25x^4+61x^3+103x^2+45x+31$
• $y^2=71x^6+61x^5+8x^4+11x^3+52x^2+x+104$
• $y^2=94x^6+94x^5+49x^4+85x^3+59x^2+14x+101$
• $y^2=57x^6+72x^5+92x^4+77x^3+97x^2+9x+58$
• $y^2=50x^6+48x^5+33x^4+41x^3+90x^2+89x+67$
• $y^2=83x^6+53x^5+86x^4+16x^3+6x^2+37x+26$
• $y^2=15x^6+11x^5+87x^4+88x^3+60x^2+52x+2$
• $y^2=x^6+33x^5+28x^4+67x^3+29x^2+6x+82$
• $y^2=10x^6+96x^5+33x^3+7x^2+65x+56$
• $y^2=101x^6+48x^5+70x^4+98x^3+86x^2+73x+12$
• and

• $y^2=55x^6+17x^5+32x^4+75x^3+71x^2+15x+28$
• $y^2=100x^6+48x^5+97x^4+101x^3+65x^2+80x+26$
• $y^2=6x^6+25x^5+13x^4+9x^3+41x^2+92x+6$
• $y^2=16x^6+62x^5+77x^4+79x^3+17x^2+5x+72$
• $y^2=85x^6+87x^5+18x^4+105x^3+35x^2+99x+91$
• $y^2=9x^6+30x^5+7x^4+52x^3+73x^2+101x+34$
• $y^2=58x^6+6x^5+12x^4+37x^3+52x^2+67x+61$
• $y^2=76x^6+11x^5+7x^4+70x^3+50x^2+101x+78$
• $y^2=67x^6+92x^5+47x^4+102x^3+50x^2+36x+18$
• $y^2=102x^6+38x^5+61x^4+20x^3+99x^2+91x+98$
• $y^2=104x^6+106x^5+13x^4+56x^3+56x^2+106x+69$
• $y^2=57x^6+10x^5+21x^4+65x^3+25x^2+100x+67$
• $y^2=67x^6+7x^5+45x^4+89x^3+80x^2+90x+39$
• $y^2=10x^6+27x^5+81x^4+105x^3+64x^2+90x+30$
• $y^2=36x^6+17x^5+19x^4+80x^3+35x^2+31x+51$
• $y^2=85x^6+68x^5+39x^4+61x^3+66x+1$
• $y^2=7x^6+104x^5+32x^4+85x^3+95x^2+83x+72$
• $y^2=12x^6+83x^5+31x^4+20x^3+61x^2+3x+28$
• $y^2=91x^6+86x^5+52x^4+9x^3+81x^2+95x+39$
• $y^2=87x^6+33x^5+64x^4+35x^3+74x^2+32x+99$
• $y^2=78x^6+83x^5+93x^4+41x^3+19x^2+52x+81$
• $y^2=3x^6+104x^5+48x^4+16x^3+106x^2+82x+26$
• $y^2=58x^6+39x^5+40x^4+13x^3+4x^2+52x+40$
• $y^2=24x^6+56x^5+48x^4+57x^3+101x^2+32x+45$
• $y^2=93x^6+56x^5+102x^4+46x^3+34x^2+41x+26$
• $y^2=11x^6+76x^5+4x^4+14x^3+60x^2+10x+38$
• $y^2=78x^6+38x^5+91x^4+14x^3+4x^2+98x+31$
• $y^2=76x^6+44x^5+65x^4+22x^3+91x^2+98x+101$
• $y^2=102x^6+47x^5+104x^4+35x^3+97x^2+62x$
• $y^2=52x^6+63x^5+53x^4+104x^3+51x^2+58x+21$
• $y^2=99x^6+7x^5+94x^4+51x^3+82x^2+8x+64$
• $y^2=64x^6+38x^5+4x^4+90x^3+103x^2+94x+61$
• $y^2=103x^6+95x^5+96x^4+96x^3+17x^2+51x+36$
• $y^2=4x^6+27x^5+17x^4+54x^3+82x^2+34x+36$
• $y^2=79x^6+47x^5+45x^4+101x^3+34x^2+65x+51$
• $y^2=5x^6+50x^5+97x^4+18x^3+12x^2+13x+33$
• $y^2=98x^6+51x^5+39x^4+41x^3+36x^2+61x+80$
• $y^2=92x^6+70x^5+37x^4+81x^3+79x^2+46x+62$
• $y^2=24x^6+103x^5+55x^4+12x^3+94x^2+27x+6$
• $y^2=12x^6+98x^5+14x^4+81x^3+37x^2+37x+74$
• $y^2=26x^6+11x^5+102x^4+100x^3+63x^2+69x+99$
• $y^2=93x^6+44x^5+87x^4+99x^3+43x^2+25x+79$
• $y^2=8x^6+102x^5+93x^4+101x^3+60x^2+41x+69$
• $y^2=42x^6+17x^5+86x^4+20x^3+50x^2+59x+45$
• $y^2=71x^6+25x^5+34x^4+6x^3+30x^2+40x+80$
• $y^2=15x^6+101x^5+100x^4+35x^3+102x^2+59x+13$
• $y^2=83x^6+16x^5+79x^4+18x^3+13x^2+68x+31$
• $y^2=67x^6+55x^5+85x^4+100x^3+103x^2+65x+55$
• $y^2=29x^6+99x^5+73x^4+3x^3+100x^2+40x+19$
• $y^2=48x^6+44x^5+79x^4+35x^3+12x^2+17x+64$
• $y^2=91x^6+2x^5+57x^4+86x^3+85x^2+16x+43$
• $y^2=34x^6+18x^5+100x^4+85x^3+32x^2+10x+44$
• $y^2=91x^6+16x^5+37x^4+22x^3+49x^2+4x+60$
• $y^2=61x^6+83x^5+97x^4+102x^3+39x^2+52x+35$
• $y^2=11x^6+50x^5+102x^4+14x^3+40x^2+42x+36$
• $y^2=12x^6+96x^5+53x^4+50x^3+102x^2+43x+46$
• $y^2=57x^6+78x^5+67x^4+7x^3+60x^2+93x+106$
• $y^2=15x^6+94x^5+30x^4+43x^3+96x^2+8x+22$
• $y^2=90x^6+34x^5+42x^4+17x^3+5x^2+85x+43$
• $y^2=19x^6+12x^5+99x^4+29x^3+16x^2+26x+103$
• $y^2=93x^6+20x^5+97x^4+x^3+83x^2+26x+28$
• $y^2=89x^6+23x^5+81x^4+99x^3+76x^2+16x+31$
• $y^2=9x^6+41x^5+51x^4+104x^3+69x^2+46x+44$
• $y^2=105x^6+106x^5+24x^4+27x^3+51x^2+103x+26$
• $y^2=56x^6+2x^5+64x^4+83x^3+51x^2+82x+3$
• $y^2=79x^6+55x^5+19x^4+88x^3+92x^2+41x+44$
• $y^2=6x^6+39x^5+14x^4+14x^3+100x^2+103x+67$
• $y^2=75x^6+22x^5+84x^4+5x^3+82x^2+52x+93$
• $y^2=105x^6+84x^5+76x^4+59x^3+79x^2+24x+29$
• $y^2=54x^6+27x^5+63x^4+9x^3+106x^2+33x+60$
• $y^2=27x^6+49x^5+68x^3+100x^2+46x+54$
• $y^2=102x^6+2x^5+52x^4+90x^3+70x^2+63x+100$
• $y^2=18x^6+58x^5+2x^4+102x^3+83x^2+64x+78$
• $y^2=2x^6+26x^5+69x^4+76x^3+97x^2+17x+21$
• $y^2=24x^6+24x^5+103x^4+71x^3+19x^2+71x+85$
• $y^2=16x^6+65x^5+101x^4+68x^3+26x^2+26x+42$
• $y^2=5x^6+59x^5+48x^4+98x^3+35x^2+73x+23$
• $y^2=64x^6+3x^5+82x^4+8x^3+38x^2+26x+28$
• $y^2=2x^6+63x^5+22x^4+7x^3+4x^2+92x+69$
• $y^2=61x^6+18x^5+87x^4+49x^3+68x^2+58x+61$
• $y^2=90x^6+47x^5+8x^4+20x^3+44x^2+60x+12$
• $y^2=12x^6+13x^5+12x^4+88x^3+48x^2+104x+10$
• $y^2=34x^6+58x^5+10x^4+69x^3+76x^2+76x+86$
• $y^2=10x^6+30x^5+80x^4+16x^3+38x^2+62x+8$
• $y^2=28x^6+105x^5+85x^4+69x^3+94x^2+94x+23$
• $y^2=105x^6+33x^5+22x^4+67x^3+102x^2+49x+56$
• $y^2=26x^6+30x^5+13x^4+51x^3+94x^2+63x+65$
• $y^2=30x^6+35x^5+3x^4+24x^3+85x^2+8x$
• $y^2=24x^6+31x^5+4x^4+x^3+15x^2+73x+48$
• $y^2=87x^6+23x^5+25x^4+56x^3+34x^2+76x+85$
• $y^2=2x^6+80x^5+39x^4+28x^3+85x^2+14x+10$
• $y^2=8x^6+33x^5+85x^4+59x^3+90x^2+50x+72$
• $y^2=57x^6+101x^5+16x^4+53x^3+62x^2+98x+98$
• $y^2=97x^6+64x^5+64x^4+65x^3+81x^2+7x+31$
• $y^2=70x^6+37x^5+50x^4+56x^3+x^2+6x+106$
• $y^2=6x^6+106x^5+46x^4+88x^3+30x^2+8x+33$
• $y^2=19x^6+33x^5+97x^4+33x^3+71x^2+8x+106$
• $y^2=31x^6+80x^5+49x^4+54x^3+52x^2+39x+23$
• $y^2=105x^6+20x^5+73x^4+98x^3+3x^2+102x+102$
• $y^2=66x^6+2x^5+71x^4+76x^3+10x^2+81x+78$
• $y^2=103x^6+86x^5+28x^4+72x^3+60x^2+15x+95$
• $y^2=86x^6+11x^5+65x^4+35x^3+11x^2+54x+61$
• $y^2=94x^6+51x^5+69x^4+45x^3+68x^2+19$
• $y^2=99x^6+22x^5+87x^4+11x^3+68x^2+6x+18$
• $y^2=25x^6+61x^5+76x^4+85x^3+62x^2+101x+28$
• $y^2=71x^6+84x^5+104x^3+34x^2+18x+18$
• $y^2=87x^6+102x^5+20x^4+62x^3+97x^2+64x+54$
• $y^2=23x^6+47x^5+2x^4+30x^3+55x^2+77x+91$

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 4.0.9655838528.1.

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.c_afc	$2$	(not in LMFDB)