Properties

Label 2.107.abj_tt
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:  $1 - 35 x + 513 x^{2} - 3745 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0698121762543$, $\pm0.246087952504$
Angle rank:  $2$ (numerical)
Number field:  4.0.3556589.1
Galois group:  $D_{4}$
Jacobians:  15

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 15 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8183 128824969 1500430027481 17182940904080861 196716107706164708368 2252190932839901277945721 25785338737593350555499041357 295216371197053272013135034397269 3379932273795303173902294543689079979 38696844627402361585101203834380827745024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 73 11251 1224799 131087835 14025586608 1500729914647 160578130432429 17181861585333699 1838459211366428863 196715135741871505686

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.3556589.1.
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.bj_tt$2$(not in LMFDB)