# Properties

 Label 2.199.abx_bly 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: $( 1 - 28 x + 199 x^{2} )( 1 - 21 x + 199 x^{2} )$ Frobenius angles: $\pm0.0391815390403$, $\pm0.232771238785$ Angle rank: $2$ (numerical) Jacobians: 16

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 16 curves, and hence is principally polarizable:

• $y^2=119x^6+101x^5+19x^4+106x^3+55x^2+161x+159$
• $y^2=190x^6+148x^5+192x^4+173x^3+129x^2+174x+122$
• $y^2=172x^6+104x^5+105x^4+113x^3+89x^2+162x+20$
• $y^2=6x^6+120x^5+93x^4+82x^3+105x^2+55x+57$
• $y^2=30x^6+31x^5+129x^4+180x^3+134x^2+27x+55$
• $y^2=70x^6+71x^5+19x^4+193x^3+159x^2+28x+164$
• $y^2=153x^6+97x^5+35x^4+173x^3+40x^2+101x+183$
• $y^2=93x^6+x^5+67x^4+60x^3+107x^2+12x+73$
• $y^2=97x^6+24x^5+188x^4+119x^3+41x^2+80x+178$
• $y^2=70x^6+194x^5+103x^4+24x^3+168x^2+116x+107$
• $y^2=123x^6+152x^5+4x^4+52x^3+170x^2+190x+143$
• $y^2=183x^6+33x^5+52x^4+39x^3+65x^2+186x+172$
• $y^2=138x^6+153x^5+120x^3+127x^2+150x+192$
• $y^2=150x^6+139x^5+25x^4+70x^3+29x^2+197x+153$
• $y^2=37x^6+81x^5+189x^4+97x^3+155x^2+39x+148$
• $y^2=57x^6+117x^5+105x^4+123x^3+152x^2+131x+39$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 30788 1551345744 62088393230864 2459386043610949440 97393696153177682225948 3856886605653843552008714496 152736579889153104294058862670188 6048521402809360705014406645775381760 239527496488516009926580018392984547308944 9485528389592790069743128567871302916821882704

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 151 39173 7878640 1568246761 312079661221 62103833973326 12358664046460939 2459374186971386161 489415464057018508240 97393677359165392443053

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
 The isogeny class factors as 1.199.abc $\times$ 1.199.av 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.ah_ahi $2$ (not in LMFDB) 2.199.h_ahi $2$ (not in LMFDB) 2.199.bx_bly $2$ (not in LMFDB) 2.199.ak_gl $3$ (not in LMFDB) 2.199.ae_bp $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.199.ah_ahi $2$ (not in LMFDB) 2.199.h_ahi $2$ (not in LMFDB) 2.199.bx_bly $2$ (not in LMFDB) 2.199.ak_gl $3$ (not in LMFDB) 2.199.ae_bp $3$ (not in LMFDB) 2.199.abm_bdb $6$ (not in LMFDB) 2.199.abg_yf $6$ (not in LMFDB) 2.199.e_bp $6$ (not in LMFDB) 2.199.k_gl $6$ (not in LMFDB) 2.199.bg_yf $6$ (not in LMFDB) 2.199.bm_bdb $6$ (not in LMFDB)