# Properties

 Label 2.64.aba_lh Base Field $\F_{2^{6}}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

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## Invariants

 Base field: $\F_{2^{6}}$ Dimension: $2$ L-polynomial: $( 1 - 15 x + 64 x^{2} )( 1 - 11 x + 64 x^{2} )$ Frobenius angles: $\pm0.113134082257$, $\pm0.258708130235$ Angle rank: $2$ (numerical) Jacobians: 48

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 48 curves, and hence is principally polarizable:

• $y^2+(x^2+x)y=(a^5+a+1)x^5+(a^5+a^4+a^3+a+1)x^4+(a^5+a+1)x^3+(a^4+1)x^2+(a^5+a^3+a)x$
• $y^2+(x^2+x)y=(a^5+a^4+a^2)x^5+(a^3+a^2)x^4+(a^5+a^4+a^2)x^3+(a^5+a)x^2+(a^5+a^3+a^2+a)x$
• $y^2+(x^2+x+a^5+a^3)y=(a^5+a^2+a+1)x^5+(a^5+a^3+a^2+1)x^4+(a^3+1)x^3+(a^5+a^3+a^2+1)x^2+(a^5+a^4+a^3+a^2+a+1)x+a^5+a$
• $y^2+(x^2+x)y=(a^4+a^2+a)x^5+(a^4+a^3+a+1)x^4+(a^4+a^2+a)x^3+(a^5+a^2+1)x^2+(a^5+a^4+a^3+a^2+a)x$
• $y^2+(x^2+x)y=(a^5+a^2)x^5+(a^4+a^3+1)x^4+(a^5+a^2)x^3+(a^4+a^2+1)x^2+(a^3+a^2)x$
• $y^2+(x^2+x+a^5+a^3+a)y=(a^5+a^2)x^5+(a^4+a^3+a^2+a+1)x^4+(a^4+a^3+a)x^3+(a^4+a^3+a^2+a+1)x^2+a^3x+a^4$
• $y^2+(x^2+x)y=(a^5+a+1)x^5+(a^5+a^3+a^2+a)x^4+(a^5+a+1)x^3+(a^5+a^2+a+1)x^2+(a^3+1)x$
• $y^2+(x^2+x+a^5+a^4+a^3+a)y=(a^4+1)x^5+(a^5+a^4+a^3+a^2)x^4+(a^4+a^3+a^2+1)x^3+(a^5+a^4+a^3+a^2)x^2+(a^3+a+1)x+a^5+a^2+a$
• $y^2+(x^2+x+a^5+a^4+a^3+a+1)y=(a^5+a^4+a+1)x^5+(a^3+a^2+a)x^4+(a^3+a+1)x^3+(a^3+a^2+a)x^2+(a^4+a^3+a^2+1)x+a^5+a^3$
• $y^2+(x^2+x)y=(a^5+1)x^5+(a^5+a^3+a^2+1)x^4+(a^5+1)x^3+(a^5+a^2+a)x^2+(a^3+a+1)x$
• $y^2+(x^2+x+a^5+a^3+a^2+a)y=(a^5+1)x^5+(a^5+a^4+a^3+a+1)x^4+(a^5+a^3)x^3+(a^5+a^4+a^3+a+1)x^2+(a^4+a^3+a+1)x+a^4$
• $y^2+(x^2+x)y=(a^5+a^2+a)x^5+a^3x^4+(a^5+a^2+a)x^3+(a^5+a^4+a+1)x^2+(a^5+a^4+a^3+a+1)x$
• $y^2+(x^2+x+a^5+a^3+a^2+a+1)y=ax^5+(a^3+a^2)x^4+(a^4+a^3+a^2+a+1)x^3+(a^3+a^2)x^2+(a^5+1)x+a^5+a^3+a$
• $y^2+(x^2+x)y=(a^5+a^4+a^2)x^5+(a^5+a^3+a+1)x^4+(a^5+a^4+a^2)x^3+(a^5+a^4+1)x^2+(a^4+a^3+a)x$
• $y^2+(x^2+x)y=(a^4+a^2)x^5+(a^4+a^3+a^2+a)x^4+(a^4+a^2)x^3+(a+1)x^2+(a^4+a^3+a^2+1)x$
• $y^2+(x^2+x+a^4+a^3+1)y=(a^5+a^4+a^2+a)x^5+(a^5+a^4+a^3+1)x^4+(a^5+a^4+a^3+a^2+1)x^3+(a^5+a^4+a^3+1)x^2+(a^4+a^3+a^2+a)x+a^5+a^4+a^3+a^2+a+1$
• $y^2+(x^2+x+a^4+a^3)y=(a+1)x^5+(a^3+a+1)x^4+(a^4+a^3+a^2+a)x^3+(a^3+a+1)x^2+(a^5+a^4+a^3+a^2+1)x+a^5+a^3+a^2$
• $y^2+(x^2+x)y=(a^2+a+1)x^5+(a^3+a^2+a)x^4+(a^2+a+1)x^3+(a^4+a^2+a+1)x^2+(a^4+a^3+1)x$
• $y^2+(x^2+x)y=(a^5+a^4)x^5+a^3x^4+(a^5+a^4)x^3+(a^4+a^2+a)x^2+(a^4+a^3+a^2+a)x$
• $y^2+(x^2+x+a^5+a^4+a^3+a^2+a)y=(a^5+a^4)x^5+(a^4+a^3+a^2+1)x^4+(a^5+a^3+a)x^3+(a^4+a^3+a^2+1)x^2+(a^5+a^3+1)x+a^4+a^3+a$
• and 28 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 2700 16416000 68794587900 281591199360000 1152978430634923500 4722379786386660384000 19342812470159589278795100 79228162322671151715125760000 324518556003408069492621952212300 1329227998721923169188366866266400000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 39 4007 262431 16784143 1073794839 68719670327 4398046364751 281474976029983 18014398639654599 1152921507154294727

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
 The isogeny class factors as 1.64.ap $\times$ 1.64.al 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 $\F_{2^{6}}$.

## 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 2.64.ae_abl $2$ (not in LMFDB) 2.64.e_abl $2$ (not in LMFDB) 2.64.ba_lh $2$ (not in LMFDB)