Properties

Label 2.113.abk_uy
Base Field $\F_{113}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $1 - 36 x + 544 x^{2} - 4068 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0881917305060$, $\pm0.238851186738$
Angle rank:  $2$ (numerical)
Number field:  4.0.4094208.2
Galois group:  $D_{4}$
Jacobians:  32

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 32 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9210 160419780 2081796358410 26586707020938000 339459915449879647050 4334524902966359905318980 55347524355089099129868254010 706732549565528990476812036096000 9024267964187181268217615100278631930 115230877654599325445327437268869244280900

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 78 12562 1442790 163061254 18424524198 2081952618514 235260543321294 26584441811918206 3004041937657675950 339456739013920454482

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.4094208.2.
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_uy$2$(not in LMFDB)