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

• Label: 2.107.abi_td
• 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:	$1 - 34 x + 497 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.110706537265$, $\pm0.251697673458$
Angle rank:	$2$ (numerical)
Number field:	4.0.6193728.2
Galois group:	$D_{4}$
Jacobians:	$14$
Isomorphism classes:	14

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8275$	$129247225$	$1501314151300$	$17184326525505625$	$196717977417428093875$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$74$	$11288$	$1225520$	$131098404$	$14025719914$	$1500731482286$	$160578148339438$	$17181861781823236$	$1838459213308459520$	$196715135756931054968$

Jacobians and polarizations

This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=21x^6+57x^5+103x^4+40x^3+26x^2+72x+26$
• $y^2=38x^6+23x^5+5x^4+63x^3+59x^2+10x+45$
• $y^2=93x^6+64x^5+36x^4+10x^3+76x^2+25x+32$
• $y^2=53x^6+6x^5+24x^4+4x^3+51x^2+88x+94$
• $y^2=38x^6+23x^5+74x^4+34x^3+70x^2+96x+64$
• $y^2=74x^6+82x^5+91x^4+49x^3+86x^2+77x+39$
• $y^2=5x^6+27x^5+41x^4+8x^3+94x^2+46x+32$
• $y^2=85x^6+38x^5+47x^4+69x^3+61x^2+105x+45$
• $y^2=50x^6+69x^5+68x^4+87x^3+87x^2+84x+43$
• $y^2=62x^6+103x^5+3x^4+92x^3+x^2+49x+45$
• $y^2=63x^6+67x^5+85x^4+24x^3+82x^2+57x+21$
• $y^2=24x^6+80x^5+4x^4+5x^3+27x^2+8x+59$
• $y^2=78x^6+42x^5+13x^4+28x^3+77x^2+106x+26$
• $y^2=50x^6+18x^5+37x^4+51x^3+87x^2+49x+31$

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 4.0.6193728.2.

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_td	$2$	(not in LMFDB)