Properties

Label 2.113.abj_ud
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:  $1 - 35 x + 523 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0830136176920$, $\pm0.261946670442$
Angle rank:  $2$ (numerical)
Number field:  4.0.9995069.2
Galois group:  $D_{4}$
Jacobians:  28

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 28 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9303 160783749 2082203944191 26586462576448341 339458235075501078768 4334521722437224185713181 55347521031788920677963935967 706732548672641949926361156460869 9024267967957693543817971473059384559 115230877662588304899621891637827510177024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 79 12591 1443073 163059755 18424432994 2081951090847 235260529195253 26584441778331379 3004041938912822299 339456739037455057086

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.9995069.2.
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_ud$2$(not in LMFDB)