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

• Label: 2.107.abj_tu
• 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:	$( 1 - 20 x + 107 x^{2} )( 1 - 15 x + 107 x^{2} )$
	$1 - 35 x + 514 x^{2} - 3745 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.0823304377774$, $\pm0.241815531636$
Angle rank:	$2$ (numerical)
Jacobians:	$24$
Isomorphism classes:	104

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8184$	$128848896$	$1500559020576$	$17183314024943616$	$196716856325169708264$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$73$	$11253$	$1224904$	$131090681$	$14025639983$	$1500730682022$	$160578139242629$	$17181861667002673$	$1838459211976344568$	$196715135745662210853$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

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

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{107}$

The isogeny class factors as 1.107.au $\times$ 1.107.ap and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.107.au : \(\Q(\sqrt{-7}) \).
• 1.107.ap : \(\Q(\sqrt{-203}) \).

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.af_adi	$2$	(not in LMFDB)
2.107.f_adi	$2$	(not in LMFDB)
2.107.bj_tu	$2$	(not in LMFDB)