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

• Label: 2.107.abm_wd
• 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:	$( 1 - 19 x + 107 x^{2} )^{2}$
	$1 - 38 x + 575 x^{2} - 4066 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.129482033963$, $\pm0.129482033963$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$7921$	$127757809$	$1498871312656$	$17182199985353881$	$196718103876227288161$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$70$	$11156$	$1223524$	$131082180$	$14025728930$	$1500734096822$	$160578196158758$	$17181862319314564$	$1838459217128398588$	$196715135762666666036$

Jacobians and polarizations

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

• $y^2=21x^6+17x^5+55x^4+68x^3+71x^2+44x+42$
• $y^2=39x^6+103x^5+102x^4+53x^3+8x^2+43x+21$
• $y^2=95x^6+41x^5+23x^4+72x^3+23x^2+41x+95$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{107}$

The isogeny class factors as 1.107.at^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-67}) \)$)$

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_afr	$2$	(not in LMFDB)
2.107.bm_wd	$2$	(not in LMFDB)
2.107.t_ju	$3$	(not in LMFDB)