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

• Label: 2.107.abi_te
• 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:	$1 - 34 x + 498 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.119970636295$, $\pm0.247044539448$
Angle rank:	$2$ (numerical)
Number field:	4.0.304400.3
Galois group:	$D_{4}$
Jacobians:	$48$
Isomorphism classes:	64

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8276$	$129271120$	$1501439442884$	$17184671849734400$	$196718616426332074756$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$74$	$11290$	$1225622$	$131101038$	$14025765474$	$1500732048970$	$160578153129902$	$17181861796950558$	$1838459212976425754$	$196715135749064739450$

Jacobians and polarizations

This isogeny class contains the Jacobians of 48 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=60x^6+14x^5+66x^4+3x^3+79x^2+30x+23$
• $y^2=103x^6+87x^5+52x^4+70x^3+7x^2+59x+94$
• $y^2=26x^6+41x^5+47x^4+17x^3+44x^2+4x+15$
• $y^2=50x^6+52x^5+31x^4+13x^3+28x^2+83x+2$
• $y^2=43x^6+73x^5+45x^4+83x^3+57x^2+2x+18$
• $y^2=12x^6+51x^5+50x^4+85x^3+3x^2+78x+41$
• $y^2=82x^6+106x^5+49x^4+88x^3+4x^2+61x+80$
• $y^2=20x^6+44x^5+65x^4+16x^3+39x^2+19x+32$
• $y^2=55x^6+104x^5+50x^4+98x^3+68x^2+22x+14$
• $y^2=2x^6+81x^5+61x^4+16x^3+55x^2+29x+7$
• $y^2=6x^6+74x^5+4x^4+86x^3+76x^2+69x+106$
• $y^2=2x^6+106x^5+29x^4+59x^3+31x^2+101x+104$
• $y^2=21x^6+89x^5+22x^4+48x^3+25x^2+3x+49$
• $y^2=64x^6+21x^5+56x^4+8x^3+28x^2+9x$
• $y^2=46x^6+71x^5+77x^4+42x^3+35x^2+103x+89$
• $y^2=29x^6+9x^5+95x^4+61x^3+102x^2+64x+3$
• $y^2=90x^6+50x^4+52x^3+40x^2+9x+103$
• $y^2=85x^6+71x^5+89x^4+24x^3+83x^2+19x+38$
• $y^2=55x^6+78x^5+46x^4+42x^3+46x^2+67x+32$
• $y^2=52x^6+18x^5+17x^4+48x^3+90x^2+22x+42$
• and

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

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 4.0.304400.3.

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_te	$2$	(not in LMFDB)