# Properties

 Label 2.199.acd_bsk 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: $( 1 - 28 x + 199 x^{2} )( 1 - 27 x + 199 x^{2} )$ Frobenius angles: $\pm0.0391815390403$, $\pm0.0936959350875$ 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 $A(\F_{q^r})$ 29756 1540051536 62034525741104 2459217132947674944 97393358188810034661476 3856886483314268838045378816 152736582268103828679132908092436 6048521415258264578822792358213137664 239527496528296194508977391087586307184304 9485528389683710389293460755493397556322698576

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 145 38885 7871800 1568139049 312078578275 62103832003406 12358664238953485 2459374192033203889 489415464138299521000 97393677360098926549325

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
 The isogeny class factors as 1.199.abc $\times$ 1.199.abb 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 are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.199.ab_anu $2$ (not in LMFDB) 2.199.b_anu $2$ (not in LMFDB) 2.199.cd_bsk $2$ (not in LMFDB) 2.199.aq_dx $3$ (not in LMFDB) 2.199.ak_acj $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.199.ab_anu $2$ (not in LMFDB) 2.199.b_anu $2$ (not in LMFDB) 2.199.cd_bsk $2$ (not in LMFDB) 2.199.aq_dx $3$ (not in LMFDB) 2.199.ak_acj $3$ (not in LMFDB) 2.199.abs_bgz $6$ (not in LMFDB) 2.199.abm_bat $6$ (not in LMFDB) 2.199.k_acj $6$ (not in LMFDB) 2.199.q_dx $6$ (not in LMFDB) 2.199.bm_bat $6$ (not in LMFDB) 2.199.bs_bgz $6$ (not in LMFDB)