# Properties

 Label 2.199.abz_boc 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: $( 1 - 28 x + 199 x^{2} )( 1 - 23 x + 199 x^{2} )$ Frobenius angles: $\pm0.0391815390403$, $\pm0.196619630811$ 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:

• $y^2=195x^6+72x^5+91x^4+173x^3+x^2+143x+72$
• $y^2=59x^5+104x^4+94x^3+142x^2+191x+28$
• $y^2=96x^6+136x^5+31x^4+98x^3+54x^2+124x+176$
• $y^2=145x^6+120x^5+165x^3+157x^2+178x+34$
• $y^2=47x^6+26x^5+134x^4+150x^3+27x+3$
• $y^2=108x^6+192x^5+189x^4+138x^3+92x^2+36x+76$
• $y^2=121x^6+175x^5+106x^4+52x^3+12x^2+105x+85$
• $y^2=191x^6+66x^5+166x^4+27x^3+23x^2+129x+147$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 30444 1547894736 62074910607696 2459362031800974144 97393740848463325045524 3856887120251138490827202816 152736582016542676442671475773764 6048521408058651258062035736304555264 239527496492990168787393881473421384473296 9485528389563662810027362232356287439827162576

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 149 39085 7876928 1568231449 312079804439 62103842259406 12358664218598441 2459374189105787089 489415464066160350272 97393677358866325188325

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
 The isogeny class factors as 1.199.abc $\times$ 1.199.ax 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.af_ajm $2$ (not in LMFDB) 2.199.f_ajm $2$ (not in LMFDB) 2.199.bz_boc $2$ (not in LMFDB) 2.199.am_fp $3$ (not in LMFDB) 2.199.ag_h $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.199.af_ajm $2$ (not in LMFDB) 2.199.f_ajm $2$ (not in LMFDB) 2.199.bz_boc $2$ (not in LMFDB) 2.199.am_fp $3$ (not in LMFDB) 2.199.ag_h $3$ (not in LMFDB) 2.199.abo_bej $6$ (not in LMFDB) 2.199.abi_zb $6$ (not in LMFDB) 2.199.g_h $6$ (not in LMFDB) 2.199.m_fp $6$ (not in LMFDB) 2.199.bi_zb $6$ (not in LMFDB) 2.199.bo_bej $6$ (not in LMFDB)