# Properties

 Label 2.113.abp_yw 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: $( 1 - 21 x + 113 x^{2} )( 1 - 20 x + 113 x^{2} )$ Frobenius angles: $\pm0.0498602789898$, $\pm0.110150159186$ 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 $A(\F_{q^r})$ 8742 158142780 2077106228568 26580296873995200 339453988615119237222 4334522465248154056200960 55347527599422953576376894198 706732558044236598713239306080000 9024267973908129343023634699280953752 115230877659056802621118685457931247403900

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 73 12381 1439536 163021937 18424202513 2081951447634 235260557111681 26584442130853153 3004041940893632128 339456739027051662861

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The isogeny class factors as 1.113.av $\times$ 1.113.au 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_ahm $2$ (not in LMFDB) 2.113.b_ahm $2$ (not in LMFDB) 2.113.bp_yw $2$ (not in LMFDB)