Properties

Label 2.107.abk_ul
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:  $1 - 36 x + 531 x^{2} - 3852 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0203849784155$, $\pm0.233794019095$
Angle rank:  $2$ (numerical)
Number field:  4.0.264208.2
Galois group:  $D_{4}$
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8093 128427817 1499671519796 17181897479561689 196714847402551439453 2252189285983373585811088 25785336141597799740508485077 295216366794605113356847501390377 3379932266831394612901524728157149012 38696844617747554855254506960406920305897

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 72 11216 1224180 131079876 14025496752 1500728817278 160578114265872 17181861329107204 1838459207578524012 196715135692791364016

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.264208.2.
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_ul$2$(not in LMFDB)