Properties

Label 2.113.abl_vr
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:  $1 - 37 x + 563 x^{2} - 4181 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0669838825484$, $\pm0.224024016429$
Angle rank:  $2$ (numerical)
Number field:  4.0.1646253.1
Galois group:  $D_{4}$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9115 159977365 2080937883355 26585612034553525 339458909531147297200 4334524103422671716938765 55347523228289371570540239835 706732546768341843437754311153925 9024267958075061041077603433973152915 115230877644483787919910929439374734931200

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 77 12527 1442195 163054539 18424469602 2081952234479 235260538531711 26584441706699251 3004041935623043825 339456738984121259582

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.1646253.1.
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.bl_vr$2$(not in LMFDB)