# Properties

 Label 2.199.abx_bmk Base Field $\F_{199}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{199}$ Dimension: $2$ L-polynomial: $( 1 - 25 x + 199 x^{2} )( 1 - 24 x + 199 x^{2} )$ Frobenius angles: $\pm0.153403448314$, $\pm0.176204172288$ 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 $A(\F_{q^r})$ 30800 1552320000 62102311409600 2459492113478400000 97394261343569930894000 3856888928577249780526080000 152736587480732574011743191772400 6048521422068557165964317229542400000 239527496521047881536737561768902184267200 9485528389593307823767194346008346791768000000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 151 39197 7880404 1568314393 312081472261 62103871377182 12358664660732779 2459374194802319953 489415464123489378076 97393677359170708537877

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
 The isogeny class factors as 1.199.az $\times$ 1.199.ay 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 $\F_{199}$.

## 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 2.199.ab_ahu $2$ (not in LMFDB) 2.199.b_ahu $2$ (not in LMFDB) 2.199.bx_bmk $2$ (not in LMFDB)