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

• Label: 2.107.abk_up
• Base field: $\F_{107}$
• Dimension: $2$
• $p$-rank: $1$
• Ordinary: no
• 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:	$1 - 36 x + 535 x^{2} - 3852 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.0971505065705$, $\pm0.211972914317$
Angle rank:	$2$ (numerical)
Number field:	4.0.909072.1
Galois group:	$D_{4}$
Jacobians:	$14$
Isomorphism classes:	14

This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

$p$-rank:	$1$
Slopes:	$[0, 1/2, 1/2, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8097$	$128523681$	$1500202346436$	$17183498036437161$	$196718250597527385177$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$72$	$11224$	$1224612$	$131092084$	$14025739392$	$1500732592414$	$160578162519840$	$17181861847570468$	$1838459212324695036$	$196715135730805275304$

Jacobians and polarizations

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

• $y^2=103x^6+45x^5+18x^4+39x^3+23x^2+103x+70$
• $y^2=3x^6+53x^5+103x^4+16x^3+80x^2+104x+84$
• $y^2=54x^6+33x^5+98x^4+63x^3+29x^2+54x+66$
• $y^2=21x^6+19x^5+66x^4+94x^3+41x^2+22x+72$
• $y^2=72x^6+37x^5+72x^4+99x^3+44x^2+100x+28$
• $y^2=75x^6+42x^5+24x^4+95x^3+26x^2+67x+13$
• $y^2=51x^6+96x^5+77x^4+102x^3+52x^2+10x+36$
• $y^2=43x^6+105x^5+49x^4+81x^3+75x^2+51x+35$
• $y^2=94x^6+37x^5+38x^4+26x^3+11x^2+80x+60$
• $y^2=10x^6+11x^5+57x^4+85x^3+21x^2+10x+33$
• $y^2=74x^6+4x^5+39x^4+83x^3+91x^2+86x+70$
• $y^2=72x^6+61x^5+93x^4+94x^3+71x^2+71x+55$
• $y^2=50x^6+36x^5+59x^4+4x^3+100x^2+82x+43$
• $y^2=15x^6+68x^5+87x^4+38x^3+82x^2+94x+60$

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 4.0.909072.1.

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.bk_up	$2$	(not in LMFDB)