Properties

Label 2.107.abk_uq
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:  $1 - 36 x + 536 x^{2} - 3852 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.112288198128$, $\pm0.203926913540$
Angle rank:  $2$ (numerical)
Number field:  4.0.499968.5
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8098 128547652 1500335061106 17183896870412304 196719088775649102178 2252196304333003958997508 25785345605309342835597008242 295216377325724308359297598636032 3379932276382061774436797736346897762 38696844624497629336653736475067518616772

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 72 11226 1224720 131095126 14025799152 1500733493898 160578173201112 17181861942027934 1838459212773454152 196715135727105319866

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.499968.5.
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_uq$2$(not in LMFDB)