# Properties

 Label 2.199.acb_bqg Base Field $\F_{199}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{199}$ Dimension: $2$ L-polynomial: $( 1 - 28 x + 199 x^{2} )( 1 - 25 x + 199 x^{2} )$ Frobenius angles: $\pm0.0391815390403$, $\pm0.153403448314$ Angle rank: $2$ (numerical) Jacobians: 8

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 8 curves, and hence is principally polarizable:

• $y^2=115x^6+80x^5+163x^4+184x^3+28x^2+10x+75$
• $y^2=166x^6+23x^5+106x^4+29x^3+15x^2+51x+155$
• $y^2=38x^6+120x^5+116x^4+174x^3+163x^2+61x+113$
• $y^2=134x^6+172x^5+106x^4+82x^3+99x^2+48x+67$
• $y^2=187x^6+107x^5+57x^4+150x^3+65x^2+67x+111$
• $y^2=13x^6+166x^5+48x^4+84x^3+81x^2+193x+108$
• $y^2=108x^6+69x^5+31x^4+93x^3+144x^2+167x+166$
• $y^2=135x^6+147x^5+153x^4+161x^3+140x^2+166x+117$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 30100 1544130000 62057080783600 2459308136954760000 97393652036485928315500 3856887241732189873464480000 152736583649918378454709992010300 6048521415641616953236583650647840000 239527496517145922027450138582368249529200 9485528389617622154801112071143558223573250000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 147 38989 7874664 1568197081 312079519857 62103844215502 12358664350762863 2459374192189077841 489415464115516684536 97393677359420358532549

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
 The isogeny class factors as 1.199.abc $\times$ 1.199.az 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.ad_alq $2$ (not in LMFDB) 2.199.d_alq $2$ (not in LMFDB) 2.199.cb_bqg $2$ (not in LMFDB) 2.199.ao_et $3$ (not in LMFDB) 2.199.ai_abb $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.199.ad_alq $2$ (not in LMFDB) 2.199.d_alq $2$ (not in LMFDB) 2.199.cb_bqg $2$ (not in LMFDB) 2.199.ao_et $3$ (not in LMFDB) 2.199.ai_abb $3$ (not in LMFDB) 2.199.abq_bfr $6$ (not in LMFDB) 2.199.abk_zx $6$ (not in LMFDB) 2.199.i_abb $6$ (not in LMFDB) 2.199.o_et $6$ (not in LMFDB) 2.199.bk_zx $6$ (not in LMFDB) 2.199.bq_bfr $6$ (not in LMFDB)