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

• Label: 2.107.abo_xq
• Base field: $\F_{107}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{107}$
Dimension:	$2$
L-polynomial:	$( 1 - 20 x + 107 x^{2} )^{2}$
	$1 - 40 x + 614 x^{2} - 4280 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.0823304377774$, $\pm0.0823304377774$
Angle rank:	$1$ (numerical)
Jacobians:	$3$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$7744$	$126877696$	$1496864159296$	$17178795458953216$	$196713315249072998464$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$68$	$11078$	$1221884$	$131056206$	$14025387508$	$1500730259222$	$160578159683884$	$17181862048951198$	$1838459216144938148$	$196715135776634581478$

Jacobians and polarizations

This isogeny class contains the Jacobians of 3 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=93x^6+94x^5+39x^4+68x^3+39x^2+94x+93$
• $y^2=58x^6+47x^4+47x^2+58$
• $y^2=5x^6+98x^4+98x^2+5$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{107}$.

Endomorphism algebra over $\F_{107}$

The isogeny class factors as 1.107.au^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-7}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.107.a_ahe	$2$	(not in LMFDB)
2.107.bo_xq	$2$	(not in LMFDB)
2.107.u_lh	$3$	(not in LMFDB)