# Properties

 Label 2.199.aca_bph 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: $( 1 - 27 x + 199 x^{2} )( 1 - 25 x + 199 x^{2} )$ Frobenius angles: $\pm0.0936959350875$, $\pm0.153403448314$ Angle rank: $2$ (numerical) Jacobians: 15

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 15 curves, and hence is principally polarizable:

• $y^2=119x^6+174x^5+107x^4+153x^3+127x^2+84x+110$
• $y^2=92x^6+191x^5+115x^4+164x^3+62x^2+71x+117$
• $y^2=55x^6+23x^5+69x^4+30x^3+118x^2+49x+78$
• $y^2=129x^6+72x^5+172x^4+156x^3+49x^2+188x+154$
• $y^2=103x^6+182x^5+102x^4+193x^3+125x^2+86x+98$
• $y^2=47x^6+183x^5+43x^4+10x^3+5x^2+48x+16$
• $y^2=79x^6+48x^5+150x^4+180x^3+186x^2+27x+175$
• $y^2=122x^6+91x^5+169x^4+63x^3+25x^2+124x+16$
• $y^2=166x^6+79x^5+101x^4+184x^3+69x^2+4x+170$
• $y^2=138x^6+157x^5+127x^4+58x^3+198x^2+155x+171$
• $y^2=154x^6+75x^5+188x^4+24x^3+9x^2+190x+39$
• $y^2=101x^6+154x^5+108x^4+189x^3+152x^2+159x+137$
• $y^2=176x^6+141x^5+193x^4+94x^3+47x^2+12x+148$
• $y^2=160x^6+78x^5+169x^4+191x^3+43x^2+143x+66$
• $y^2=165x^6+22x^5+40x^4+73x^3+72x^2+127x+23$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 30275 1546295625 62070255976400 2459369981558975625 97393902266009290893875 3856888155503483602296480000 152736586731691134556253029655075 6048521425354997856439716269132255625 239527496545898703464486168504741421630800 9485528389697488101927268042493993509095515625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 148 39044 7876336 1568236516 312080321668 62103858929102 12358664600124172 2459374196138611396 489415464174265914064 97393677360240390687524

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
 The isogeny class factors as 1.199.abb $\times$ 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 is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.199.ac_akr $2$ (not in LMFDB) 2.199.c_akr $2$ (not in LMFDB) 2.199.ca_bph $2$ (not in LMFDB)