Properties

Label 2.113.abj_ul
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:  $1 - 35 x + 531 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.160388096429$, $\pm0.219985207361$
Angle rank:  $2$ (numerical)
Number field:  4.0.483725.1
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9311 160996501 2083419015479 26590104987836021 339465560665668705136 4334532286964374506771181 55347531251384888752574905799 706732551822980837900767966590725 9024267956614688814152385386526890471 115230877633100602274318742520654161700096

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 79 12607 1443913 163082091 18424830594 2081956165183 235260572634733 26584441896834483 3004041935136908059 339456738950587721022

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.483725.1.
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_ul$2$(not in LMFDB)