Properties

Label 2.113.abk_uw
Base field $\F_{113}$
Dimension $2$
$p$-rank $2$
Ordinary Yes
Supersingular No
Simple Yes
Geometrically simple Yes
Primitive Yes
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $1 - 36 x + 542 x^{2} - 4068 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0642676148061$, $\pm0.247058548138$
Angle rank:  $2$ (numerical)
Number field:  4.0.64512.5
Galois group:  $D_{4}$
Jacobians:  28

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 28 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9208 160366528 2081483878648 26585724661300224 339457773048401796088 4334521320135267660661696 55347519571922474835090446584 706732544419420817805210404241408 9024267959757945226071833273684774392 115230877651500338842173605009348646935488

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 78 12558 1442574 163055230 18424407918 2081950897614 235260522989934 26584441618342270 3004041936183250446 339456739004791201038

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.64512.5.
All geometric endomorphisms are defined over $\F_{113}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.bk_uw$2$(not in LMFDB)