Properties

Label 2.113.abn_xh
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:  $1 - 39 x + 605 x^{2} - 4407 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0784394555333$, $\pm0.167562406750$
Angle rank:  $2$ (numerical)
Number field:  4.0.76725.1
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8929 159123709 2079422316409 26584264839081141 339459443628842308864 4334528553978043026275101 55347532752408115210035321169 706732560224911260203707837953189 9024267971181897152754045932532582841 115230877650424305847101883920807305089024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 75 12459 1441143 163046275 18424498590 2081954372163 235260579014991 26584442212881379 3004041939986110779 339456739001621333214

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.76725.1.
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.bn_xh$2$(not in LMFDB)