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

• Label: 2.107.abi_th
• 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:	$1 - 34 x + 501 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.150645107453$, $\pm0.228428208090$
Angle rank:	$2$ (numerical)
Number field:	4.0.1053248.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8279$	$129342817$	$1501815335588$	$17185704687927689$	$196720504845327107599$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$74$	$11296$	$1225928$	$131108916$	$14025900114$	$1500733660078$	$160578164865206$	$17181861783319524$	$1838459210936854664$	$196715135710800036816$

Jacobians and polarizations

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

• $y^2=69x^6+18x^5+21x^4+41x^3+92x^2+8x+77$
• $y^2=56x^6+69x^5+45x^4+69x^3+29x^2+46x+3$
• $y^2=22x^6+97x^5+103x^4+90x^3+79x^2+66x+87$
• $y^2=10x^6+39x^5+53x^4+42x^3+84x^2+74x+28$
• $y^2=58x^6+75x^5+20x^4+24x^3+37x^2+82x+63$
• $y^2=77x^6+89x^5+16x^4+22x^3+82x^2+100x+7$
• $y^2=8x^6+75x^5+52x^4+92x^3+47x^2+47x+41$
• $y^2=43x^6+69x^5+71x^4+6x^3+77x^2+95x+63$
• $y^2=62x^6+26x^5+92x^4+31x^3+26x^2+22x+52$
• $y^2=84x^6+34x^5+86x^4+9x^3+12x^2+77x+60$
• $y^2=95x^6+106x^5+38x^4+83x^3+25x^2+35x+63$
• $y^2=46x^6+67x^5+5x^4+51x^3+5x^2+105x+67$

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 4.0.1053248.1.

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.bi_th	$2$	(not in LMFDB)