# Properties

 Label 2.169.abs_bfh Base Field $\F_{13^{2}}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{13^{2}}$ Dimension: $2$ L-polynomial: $( 1 - 25 x + 169 x^{2} )( 1 - 19 x + 169 x^{2} )$ Frobenius angles: $\pm0.0885687144757$, $\pm0.239161554446$ Angle rank: $2$ (numerical) Jacobians: 84

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 84 curves, and hence is principally polarizable:

• $y^2=(12a+11)x^6+(9a+11)x^5+(6a+10)x^4+(8a+6)x^3+(6a+10)x^2+(9a+11)x+12a+11$
• $y^2=(12a+6)x^6+(11a+7)x^5+2x^4+(12a+4)x^3+2x^2+(11a+7)x+12a+6$
• $y^2=(11a+2)x^6+(a+3)x^5+(4a+2)x^4+(3a+9)x^3+7x^2+(10a+4)x+4a+9$
• $y^2=(10a+9)x^6+(10a+11)x^5+(a+7)x^4+(7a+4)x^3+6x^2+(6a+7)x+a+7$
• $y^2=(7a+1)x^6+(7a+5)x^5+(10a+6)x^4+(4a+11)x^3+(10a+6)x^2+(7a+5)x+7a+1$
• $y^2=(12a+11)x^6+(6a+5)x^5+(8a+11)x^4+ax^3+(8a+11)x^2+(6a+5)x+12a+11$
• $y^2=(2a+9)x^6+(a+5)x^5+(11a+4)x^4+(12a+11)x^3+(a+9)x^2+2x+7a+5$
• $y^2=(10a+3)x^6+(10a+5)x^5+11ax^4+(2a+8)x^3+(10a+10)x^2+(8a+10)x+8a+12$
• $y^2=(3a+3)x^6+(12a+1)x^5+(7a+9)x^4+(2a+12)x^3+(7a+9)x^2+(12a+1)x+3a+3$
• $y^2=(4a+4)x^6+(3a+11)x^5+(4a+5)x^4+(3a+12)x^3+(7a+12)x^2+(a+1)x+2a+12$
• $y^2=(a+1)x^6+(5a+2)x^5+(2a+7)x^4+(9a+2)x^3+(9a+12)x^2+(5a+5)x+a+7$
• $y^2=(a+1)x^6+(7a+10)x^5+(8a+11)x^4+(9a+9)x^3+(2a+4)x^2+(2a+5)x+5a+11$
• $y^2=(10a+9)x^6+9ax^5+(9a+4)x^4+(12a+3)x^3+(9a+7)x^2+(10a+7)x+8a+3$
• $y^2=(4a+9)x^6+(a+1)x^5+(9a+12)x^4+(8a+12)x^3+(9a+12)x^2+(a+1)x+4a+9$
• $y^2=(a+12)x^6+(4a+12)x^5+(6a+6)x^4+(6a+6)x^3+(6a+6)x^2+(4a+12)x+a+12$
• $y^2=(7a+12)x^6+x^5+(3a+6)x^4+3ax^3+2x^2+(4a+12)x+a+10$
• $y^2=(4a+11)x^6+(6a+9)x^5+(12a+9)x^4+(8a+3)x^3+(12a+9)x^2+(6a+9)x+4a+11$
• $y^2=(2a+11)x^6+(6a+8)x^5+(6a+3)x^4+(9a+12)x^3+(2a+2)x^2+(10a+7)x+a+1$
• $y^2=10ax^6+(6a+6)x^5+(12a+7)x^4+(12a+1)x^3+(12a+7)x^2+(6a+6)x+10a$
• $y^2=(a+2)x^6+(9a+12)x^5+(2a+2)x^3+(10a+4)x^2+(8a+5)x+7a+3$
• and 64 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 21895 806940225 23297237074240 665442179281049625 19005029097392428768975 542800838163925329227366400 15502932727505618878876326332335 442779263392725118306696807596299625 12646218552530437566099693034715838287680 361188648087687213175678648240886685643580625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 126 28252 4826634 815762068 137858965686 23298088032142 3937376366611254 665416608605924068 112455406950179714106 19004963775046849071052

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
 The isogeny class factors as 1.169.az $\times$ 1.169.at 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 $\F_{13^{2}}$.

## 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 2.169.ag_afh $2$ (not in LMFDB) 2.169.g_afh $2$ (not in LMFDB) 2.169.bs_bfh $2$ (not in LMFDB)