Properties

Label 2.113.abj_uf
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:  $1 - 35 x + 525 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.101307485312$, $\pm0.254747453785$
Angle rank:  $2$ (numerical)
Number field:  4.0.8663141.1
Galois group:  $D_{4}$
Jacobians:  27

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 27 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9305 160836925 2082507693065 26587377079743125 339460105159131270400 4334524560112221010269325 55347524267287002563076892385 706732551249414021036375741993125 9024267968872428095665975350510830945 115230877661590421325689788664051653120000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 79 12595 1443283 163065363 18424534494 2081952453835 235260542948083 26584441875259203 3004041939217323559 339456739034515408350

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.8663141.1.
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.bj_uf$2$(not in LMFDB)