# Properties

 Label 2.113.abn_xi Base Field $\F_{113}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{113}$ Dimension: $2$ L-polynomial: $( 1 - 20 x + 113 x^{2} )( 1 - 19 x + 113 x^{2} )$ Frobenius angles: $\pm0.110150159186$, $\pm0.148111132014$ Angle rank: $2$ (numerical) Jacobians: 0

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 is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8930 159150460 2079591681440 26584862067467200 339460963390899099650 4334531653823464409854720 55347538064423423022131434610 706732567999365850480768214880000 9024267980793842192578591072385225120 115230877659853536237764329224342211402300

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 75 12461 1441260 163049937 18424581075 2081955861074 235260601594275 26584442505325153 3004041943185781500 339456739029398747261

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The isogeny class factors as 1.113.au $\times$ 1.113.at 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.
 Twist Extension Degree Common base change 2.113.ab_afy $2$ (not in LMFDB) 2.113.b_afy $2$ (not in LMFDB) 2.113.bn_xi $2$ (not in LMFDB)