Properties

Label 2.107.abk_un
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:  $1 - 36 x + 533 x^{2} - 3852 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0666671800057$, $\pm0.224228209066$
Angle rank:  $2$ (numerical)
Number field:  4.0.1025.1
Galois group:  $D_{4}$
Jacobians:  22

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 22 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8095 128475745 1499936926720 17182698802220025 196716559096562407375 2252192169535502631239680 25785340193913022680432068695 295216371735350854443245222402025 3379932272295706684201617285258603520 38696844623625589219285800319644813978625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 72 11220 1224396 131085988 14025618792 1500730738710 160578139501656 17181861616663108 1838459210550747732 196715135722672310100

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.1025.1.
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_un$2$(not in LMFDB)