Properties

Label 2.107.abh_sd
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:  $1 - 33 x + 471 x^{2} - 3531 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0527134479232$, $\pm0.291652687618$
Angle rank:  $2$ (numerical)
Number field:  4.0.11657893.2
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
$A(\F_{q^r})$ 8357 129408145 1500850101647 17182094630854525 196713323262495970352 2252186983346249666713945 25785335838935143115023644971 295216371506205020217537493751925 3379932277238393007242993166621326393 38696844630661023196107206828815255033600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 75 11303 1225143 131081379 14025388080 1500727282931 160578112381041 17181861603326611 1838459213239241601 196715135758436888918

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.11657893.2.
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.bh_sd$2$(not in LMFDB)