Properties

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

Learn more about

Invariants

Base field:  $\F_{107}$
Dimension:  $2$
L-polynomial:  $1 - 34 x + 501 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.150645107453$, $\pm0.228428208090$
Angle rank:  $2$ (numerical)
Number field:  4.0.1053248.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8279 129342817 1501815335588 17185704687927689 196720504845327107599 2252196553724261982844048 25785344266744691207425725863 295216374598818320627154756696137 3379932273005548529416119526834502468 38696844621290133369107341991353424187697

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 74 11296 1225928 131108916 14025900114 1500733660078 160578164865206 17181861783319524 1838459210936854664 196715135710800036816

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.1053248.1.
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.bi_th$2$(not in LMFDB)