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

• Label: 2.107.abi_sx
• 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:	$1 - 34 x + 491 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.0468897983382$, $\pm0.272970800803$
Angle rank:	$2$ (numerical)
Number field:	4.0.325008.5
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8269$	$129103897$	$1500562464208$	$17182243608572809$	$196714043236242414949$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$74$	$11276$	$1224908$	$131082516$	$14025439414$	$1500727770038$	$160578110270386$	$17181861478414564$	$1838459211394905044$	$196715135744751201116$

Jacobians and polarizations

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

• $y^2=24x^6+64x^5+9x^4+75x^3+47x^2+48x+38$
• $y^2=49x^6+14x^5+4x^4+18x^3+74x^2+105x+70$
• $y^2=71x^6+98x^5+43x^4+16x^3+103x^2+45x+51$
• $y^2=82x^6+4x^5+80x^4+102x^3+79x^2+6x+103$
• $y^2=49x^6+95x^5+30x^4+32x^3+41x^2+59x+97$
• $y^2=91x^6+2x^5+39x^4+99x^3+11x^2+85x+22$
• $y^2=68x^6+25x^5+40x^4+4x^3+95x^2+21x+54$
• $y^2=39x^6+32x^5+28x^4+39x^3+x^2+47x+77$
• $y^2=98x^6+54x^5+23x^4+66x^3+74x^2+43x+8$
• $y^2=82x^6+19x^5+16x^4+6x^3+95x^2+2x+97$
• $y^2=80x^6+31x^5+36x^4+4x^3+52x^2+82x+106$
• $y^2=29x^6+71x^5+81x^4+54x^3+94x^2+75x+92$

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 4.0.325008.5.

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_sx	$2$	(not in LMFDB)