Properties

Label 2.107.abk_um
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:  $1 - 36 x + 532 x^{2} - 3852 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0483974556481$, $\pm0.229252355639$
Angle rank:  $2$ (numerical)
Number field:  4.0.1052928.2
Galois group:  $D_{4}$
Jacobians:  20

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 20 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8094 128451780 1499804221662 17182298401952400 196715705773693935054 2252190740473495245171780 25785338212389043858171403118 295216369387493073680449873612800 3379932269843026349204268733239129918 38696844621236712148279371172427669376900

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 72 11218 1224288 131082934 14025557952 1500729786466 160578127161720 17181861480015646 1838459209216652136 196715135710528470418

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.1052928.2.
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.bk_um$2$(not in LMFDB)