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

• Label: 2.107.abk_us
• Base field: $\F_{107}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{107}$
Dimension:	$2$
L-polynomial:	$( 1 - 18 x + 107 x^{2} )^{2}$
	$1 - 36 x + 538 x^{2} - 3852 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.164078095836$, $\pm0.164078095836$
Angle rank:	$1$ (numerical)
Jacobians:	$36$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8100$	$128595600$	$1500600500100$	$17184692972160000$	$196720749987234502500$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$72$	$11230$	$1224936$	$131101198$	$14025917592$	$1500735246190$	$160578192915576$	$17181862089443998$	$1838459212816753512$	$196715135704944961150$

Jacobians and polarizations

This isogeny class contains the Jacobians of 36 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=106x^6+100x^5+89x^4+42x^3+9x^2+25x+67$
• $y^2=89x^6+106x^4+106x^2+89$
• $y^2=41x^6+91x^5+76x^4+36x^3+76x^2+91x+41$
• $y^2=62x^6+30x^5+95x^4+89x^3+95x^2+30x+62$
• $y^2=78x^6+90x^5+79x^4+35x^3+81x^2+11x+97$
• $y^2=98x^6+12x^5+86x^4+63x^3+27x^2+105x+21$
• $y^2=97x^6+58x^4+58x^2+97$
• $y^2=59x^6+79x^5+92x^4+27x^3+42x^2+33x+77$
• $y^2=21x^6+7x^5+81x^4+72x^3+27x^2+84x+84$
• $y^2=72x^6+22x^5+9x^3+22x+72$
• $y^2=20x^6+99x^5+73x^4+76x^3+73x^2+99x+20$
• $y^2=49x^6+21x^5+20x^4+58x^3+80x^2+15x+33$
• $y^2=37x^6+67x^5+92x^4+38x^3+92x^2+67x+37$
• $y^2=83x^6+31x^5+17x^4+104x^3+17x^2+31x+83$
• $y^2=20x^6+27x^5+32x^4+91x^3+32x^2+27x+20$
• $y^2=70x^6+35x^5+90x^4+23x^3+56x^2+101x+71$
• $y^2=95x^6+68x^4+68x^2+95$
• $y^2=46x^6+20x^5+14x^4+38x^3+15x^2+35x+21$
• $y^2=101x^6+74x^5+82x^4+42x^3+45x^2+60x+29$
• $y^2=12x^6+32x^5+92x^4+57x^3+92x^2+32x+12$
• and

• $y^2=28x^6+68x^5+22x^4+12x^3+22x^2+68x+28$
• $y^2=21x^6+92x^5+24x^4+97x^3+24x^2+92x+21$
• $y^2=21x^6+27x^5+11x^4+24x^3+41x^2+9x+65$
• $y^2=35x^6+15x^5+19x^4+100x^3+27x^2+12x+71$
• $y^2=22x^6+19x^5+78x^4+10x^3+103x^2+101x+74$
• $y^2=95x^6+87x^5+7x^4+27x^3+7x^2+87x+95$
• $y^2=43x^6+96x^5+98x^4+32x^3+82x^2+71x+31$
• $y^2=104x^6+70x^5+55x^4+17x^3+54x^2+91x+95$
• $y^2=65x^6+36x^5+50x^4+52x^3+50x^2+36x+65$
• $y^2=65x^6+49x^5+95x^4+100x^3+95x^2+49x+65$
• $y^2=96x^6+96x^5+26x^4+6x^3+26x^2+96x+96$
• $y^2=101x^6+38x^5+33x^4+28x^3+101x^2+26x+17$
• $y^2=20x^6+7x^5+97x^3+45x+106$
• $y^2=106x^6+34x^5+98x^4+75x^3+98x^2+34x+106$
• $y^2=77x^6+73x^5+11x^4+56x^3+3x^2+24x+67$
• $y^2=97x^6+79x^5+7x^4+24x^3+63x^2+86x+93$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{107}$

The isogeny class factors as 1.107.as^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-26}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.107.a_aeg	$2$	(not in LMFDB)
2.107.bk_us	$2$	(not in LMFDB)
2.107.s_ij	$3$	(not in LMFDB)