# Properties

 Label 2.49.aw_ik Base Field $\F_{7^{2}}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{7^{2}}$ Dimension: $2$ L-polynomial: $( 1 - 12 x + 49 x^{2} )( 1 - 10 x + 49 x^{2} )$ Frobenius angles: $\pm0.172237328522$, $\pm0.246751714429$ Angle rank: $2$ (numerical) Jacobians: 16

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 16 curves, and hence is principally polarizable:

• $y^2=2x^6+(3a+3)x^5+(5a+4)x^4+(a+4)x^3+(3a+1)x^2+(5a+5)x+2$
• $y^2=(3a+1)x^6+(a+3)x^5+(3a+2)x^4+6x^3+(3a+2)x^2+(a+3)x+3a+1$
• $y^2=4ax^6+(4a+2)x^5+(a+1)x^4+4x^3+(5a+5)x^2+(2a+1)x+3a$
• $y^2=(3a+5)x^6+(4a+4)x^5+(4a+3)x^4+3x^3+(a+6)x^2+(2a+2)x+3a+5$
• $y^2=6ax^6+(6a+2)x^5+2x^3+(3a+4)x+6a+1$
• $y^2=(5a+5)x^6+6x^5+(3a+4)x^4+(2a+3)x^3+6ax^2+(3a+2)x+5a+4$
• $y^2=5ax^6+(3a+1)x^5+(4a+6)x^4+(4a+4)x^3+(4a+6)x^2+(3a+1)x+5a$
• $y^2=4ax^6+5x^5+(6a+6)x^4+(6a+3)x^3+(2a+2)x^2+6x+3a$
• $y^2=6ax^6+(2a+5)x^5+(3a+5)x^3+(2a+3)x+4a+6$
• $y^2=(3a+1)x^6+(2a+4)x^5+(a+5)x^4+(6a+2)x^3+(a+5)x^2+(2a+4)x+3a+1$
• $y^2=(5a+6)x^6+(4a+1)x^5+(5a+2)x^4+(3a+2)x^3+(5a+2)x^2+(4a+1)x+5a+6$
• $y^2=(a+6)x^6+(6a+3)x^5+4x^4+(a+6)x^3+4x^2+(6a+3)x+a+6$
• $y^2=(2a+3)x^6+6x^5+4ax^4+(5a+5)x^3+(a+6)x^2+(4a+5)x+2a+2$
• $y^2=(5a+5)x^6+(3a+1)x^5+(2a+3)x^4+x^3+(2a+3)x^2+(3a+1)x+5a+5$
• $y^2=6ax^6+(5a+4)x^4+(4a+3)x^3+(5a+4)x^2+6a$
• $y^2=(3a+2)x^6+4x^5+(5a+4)x^4+(a+6)x^3+(5a+4)x^2+4x+3a+2$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 1520 5654400 13901070320 33276098764800 79807921836143600 191584669587359126400 459986696959355624971760 1104427435757914105705267200 2651730724182108519258040237040 6366805727324421151255906048560000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 28 2354 118156 5772286 282530668 13841535602 678223309372 33232923393406 1628413523188924 79792265876711474

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7^{2}}$
 The isogeny class factors as 1.49.am $\times$ 1.49.ak 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 $\F_{7^{2}}$.

## 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 2.49.ac_aw $2$ (not in LMFDB) 2.49.c_aw $2$ (not in LMFDB) 2.49.w_ik $2$ (not in LMFDB)