Properties

Label 2.113.abm_wk
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:  $1 - 38 x + 582 x^{2} - 4294 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0151964286034$, $\pm0.210853355850$
Angle rank:  $2$ (numerical)
Number field:  4.0.4400.1
Galois group:  $D_{4}$
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9020 159509680 2079923613020 26584023637318400 339456808270912865500 4334521378749489394991920 55347519192888865718192533820 706732539834360918602977162342400 9024267945821559123211229992401868220 115230877624335369116273262703055750782000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 76 12490 1441492 163044798 18424355556 2081950925770 235260521378812 26584441445870718 3004041931544038876 339456738924766365450

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.4400.1.
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.bm_wk$2$(not in LMFDB)