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

• Label: 2.107.abj_tw
• 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:	$1 - 35 x + 516 x^{2} - 3745 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.105531336350$, $\pm0.231854495772$
Angle rank:	$2$ (numerical)
Number field:	4.0.2485400.1
Galois group:	$D_{4}$
Jacobians:	$12$
Isomorphism classes:	12

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8186$	$128896756$	$1500817016024$	$17184058699816736$	$196718338838794302886$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$73$	$11257$	$1225114$	$131096361$	$14025745683$	$1500732169138$	$160578155372449$	$17181861794350353$	$1838459212486426798$	$196715135741446503897$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=78x^6+87x^5+50x^4+35x^3+45x^2+86x+59$
• $y^2=106x^6+10x^5+59x^4+92x^3+63x^2+36x+89$
• $y^2=103x^6+106x^5+22x^4+2x^3+6x^2+24x+22$
• $y^2=95x^6+33x^5+74x^4+2x^3+50x^2+52x+91$
• $y^2=19x^6+82x^5+95x^4+x^3+90x^2+93x+71$
• $y^2=67x^6+71x^5+19x^4+27x^3+68x^2+10x+50$
• $y^2=19x^6+63x^5+48x^4+70x^3+25x^2+53x+48$
• $y^2=73x^6+86x^5+16x^4+94x^3+12x^2+21x+96$
• $y^2=18x^6+97x^5+7x^4+11x^3+28x^2+85x+56$
• $y^2=32x^6+103x^5+35x^4+66x^3+2x^2+73x+56$
• $y^2=74x^6+76x^5+81x^4+36x^3+85x^2+18x+62$
• $y^2=48x^6+46x^5+86x^4+31x^3+82x^2+8x+21$

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 4.0.2485400.1.

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.bj_tw	$2$	(not in LMFDB)