Properties

 Label 2.199.abx_bmi 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: $( 1 - 26 x + 199 x^{2} )( 1 - 23 x + 199 x^{2} )$ Frobenius angles: $\pm0.126927281034$, $\pm0.196619630811$ Angle rank: $2$ (numerical) Jacobians: 12

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 12 curves, and hence is principally polarizable:

• $y^2=108x^6+198x^5+178x^4+167x^3+102x^2+45x+17$
• $y^2=65x^6+65x^5+4x^4+111x^3+180x^2+20x+124$
• $y^2=182x^6+75x^5+182x^4+136x^3+149x^2+115x+183$
• $y^2=149x^6+178x^5+182x^4+62x^3+54x^2+148x+120$
• $y^2=38x^6+23x^5+14x^4+88x^3+187x^2+137x+30$
• $y^2=12x^6+8x^5+144x^4+98x^3+179x^2+26$
• $y^2=65x^6+168x^5+87x^4+42x^3+145x^2+111x+48$
• $y^2=38x^6+118x^5+17x^4+181x^3+37x^2+114x+196$
• $y^2=x^6+123x^5+29x^4+111x^3+76x^2+136x+35$
• $y^2=81x^6+9x^5+122x^4+127x^3+75x^2+13x+187$
• $y^2=166x^6+185x^5+101x^4+109x^3+29x^2+134x+182$
• $y^2=22x^6+17x^5+113x^4+26x^3+108x^2+50x+77$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 30798 1552157604 62099991653544 2459474497819712160 97394168674300405771098 3856888560860574883797231936 152736586386810577825410738934938 6048521420029713448659036837706803840 239527496522186117495283705500825185877064 9485528389624232532353831810951367976709609604

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 151 39193 7880110 1568303161 312081175321 62103865456186 12358664572218199 2459374193973310801 489415464125815083010 97393677359488231291153

Decomposition and endomorphism algebra

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