Properties

Label 2.113.abk_uv
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:  $( 1 - 21 x + 113 x^{2} )( 1 - 15 x + 113 x^{2} )$
Frobenius angles:  $\pm0.0498602789898$, $\pm0.250704227710$
Angle rank:  $2$ (numerical)
Jacobians:  35

This isogeny class is not 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 35 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9207 160339905 2081327643648 26585232506580825 339456691899909109647 4334519476192466926632960 55347516988609419659410122303 706732541304286735260718731275625 9024267956283398383374651784318835712 115230877647455556053704680937196533607025

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 78 12556 1442466 163052212 18424349238 2081950011934 235260512009286 26584441501163428 3004041935026626498 339456738992875742236

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.av $\times$ 1.113.ap and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ag_adl$2$(not in LMFDB)
2.113.g_adl$2$(not in LMFDB)
2.113.bk_uv$2$(not in LMFDB)