Properties

Label 2.107.abj_tv
Base Field $\F_{107}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{107}$
Dimension:  $2$
L-polynomial:  $1 - 35 x + 515 x^{2} - 3745 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0940700217071$, $\pm0.237116005334$
Angle rank:  $2$ (numerical)
Number field:  4.0.3149181.2
Galois group:  $D_{4}$
Jacobians:  16

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains the Jacobians of 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8185 128872825 1500688016755 17183686623518125 196717600036042370800 2252193212251610993585425 25785341487180839316840231895 295216373796844595511525224743125 3379932275600495426409710421947024965 38696844628111358827450621961597123680000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 73 11255 1225009 131093523 14025693008 1500731433515 160578147555479 17181861736643923 1838459212348333843 196715135745475688150

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.3149181.2.
All geometric endomorphisms are defined over $\F_{107}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.107.bj_tv$2$(not in LMFDB)