# Properties

 Label 2.199.acc_brj 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: $( 1 - 27 x + 199 x^{2} )^{2}$ Frobenius angles: $\pm0.0936959350875$, $\pm0.0936959350875$ Angle rank: $1$ (numerical) Jacobians: 3

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 3 curves, and hence is principally polarizable:

• $y^2=152x^6+131x^5+96x^4+152x^3+96x^2+131x+152$
• $y^2=119x^6+131x^5+166x^4+137x^3+182x^2+133x+115$
• $y^2=31x^6+41x^5+151x^4+79x^3+57x^2+67x+3$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 29929 1542211441 62047696145296 2459278975263398649 97393608417578426434849 3856887397085382882981673216 152736585349876556899743089181409 6048521424971645481410295572923093929 239527496557048975947351895098681903194896 9485528389763576336420173174436926777076824801

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 146 38940 7873472 1568178484 312079380086 62103846717006 12358664488314794 2459374195982737444 489415464197048750528 97393677360918958704300

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
 The isogeny class factors as 1.199.abb 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-67})$$$)$
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.a_amt $2$ (not in LMFDB) 2.199.cc_brj $2$ (not in LMFDB) 2.199.bb_uk $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.199.a_amt $2$ (not in LMFDB) 2.199.cc_brj $2$ (not in LMFDB) 2.199.bb_uk $3$ (not in LMFDB) 2.199.a_mt $4$ (not in LMFDB) 2.199.abb_uk $6$ (not in LMFDB)