# Properties

 Label 2.199.acc_bri 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: $( 1 - 28 x + 199 x^{2} )( 1 - 26 x + 199 x^{2} )$ Frobenius angles: $\pm0.0391815390403$, $\pm0.126927281034$ 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:

• $y^2=143x^6+9x^5+198x^4+189x^3+156x^2+124x+34$
• $y^2=8x^6+187x^5+46x^4+158x^3+177x^2+115x+103$
• $y^2=2x^6+196x^5+142x^4+70x^3+142x^2+196x+2$
• $y^2=85x^6+119x^5+100x^4+14x^3+26x^2+192x+138$
• $y^2=73x^6+96x^5+171x^4+105x^3+171x^2+96x+73$
• $y^2=16x^6+9x^5+75x^4+188x^3+75x^2+9x+16$
• $y^2=15x^6+17x^5+170x^4+198x^3+12x^2+134x+186$
• $y^2=109x^6+8x^5+180x^4+156x^3+180x^2+8x+109$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 29928 1542129984 62046417540744 2459267748751656960 97393535783741510069448 3856887010152228461786185536 152736583556598983041184406574248 6048521417515945877455928005581373440 239527496528739361782742956437691674685864 9485528389664414164494146947187207664835408704

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 146 38938 7873310 1568171326 312079147346 62103840486586 12358664343211934 2459374192951194046 489415464139205024210 97393677359900800497178

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
 The isogeny class factors as 1.199.abc $\times$ 1.199.aba 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.ac_ams $2$ (not in LMFDB) 2.199.c_ams $2$ (not in LMFDB) 2.199.cc_bri $2$ (not in LMFDB) 2.199.ap_ei $3$ (not in LMFDB) 2.199.aj_abs $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.199.ac_ams $2$ (not in LMFDB) 2.199.c_ams $2$ (not in LMFDB) 2.199.cc_bri $2$ (not in LMFDB) 2.199.ap_ei $3$ (not in LMFDB) 2.199.aj_abs $3$ (not in LMFDB) 2.199.abr_bgi $6$ (not in LMFDB) 2.199.abl_bai $6$ (not in LMFDB) 2.199.j_abs $6$ (not in LMFDB) 2.199.p_ei $6$ (not in LMFDB) 2.199.bl_bai $6$ (not in LMFDB) 2.199.br_bgi $6$ (not in LMFDB)