Properties

Label 2.107.abi_tg
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:  $1 - 34 x + 500 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.139535173173$, $\pm0.235768451684$
Angle rank:  $2$ (numerical)
Number field:  4.0.2164032.9
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
$A(\F_{q^r})$ 8278 129318916 1501690035022 17185360930933456 196719880140270695758 2252195770005975486666532 25785343708920516336327225238 295216374844384122386618410595328 3379932274568536957215552018689574214 38696844624257683451461539526751494055716

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 74 11294 1225826 131106294 14025855574 1500733137854 160578161391358 17181861797611678 1838459211787016810 196715135725885556654

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.2164032.9.
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.bi_tg$2$(not in LMFDB)