Invariants
Base field: | $\F_{11^{2}}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 21 x + 121 x^{2} )( 1 - 15 x + 121 x^{2} )$ |
$1 - 36 x + 557 x^{2} - 4356 x^{3} + 14641 x^{4}$ | |
Frobenius angles: | $\pm0.0963413489042$, $\pm0.261189521777$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $44$ |
Isomorphism classes: | 80 |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $10807$ | $211719937$ | $3139193843968$ | $45953732930873625$ | $672754298622262473727$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $86$ | $14460$ | $1771994$ | $214377556$ | $25937590526$ | $3138428495022$ | $379749820441406$ | $45949729773931876$ | $5559917315671205354$ | $672749995001954839980$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 44 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=(4a+2)x^6+(9a+5)x^5+(a+9)x^4+(10a+7)x^3+(a+9)x^2+(9a+5)x+4a+2$
- $y^2=(7a+6)x^6+(4a+4)x^5+(4a+5)x^4+(5a+4)x^3+(7a+1)x^2+(6a+6)x+8a+5$
- $y^2=(8a+4)x^6+(8a+7)x^5+ax^4+(9a+5)x^3+(3a+7)x^2+5ax+4$
- $y^2=(3a+7)x^6+(4a+1)x^5+(3a+4)x^4+(3a+1)x^3+(5a+3)x^2+3x+6a+9$
- $y^2=(9a+9)x^6+(3a+9)x^5+(8a+5)x^4+(a+3)x^3+(10a+2)x^2+6ax+4a+6$
- $y^2=(5a+8)x^6+(3a+4)x^5+(7a+10)x^4+(7a+1)x^3+(8a+5)x^2+(6a+1)x+a+7$
- $y^2=x^6+(5a+1)x^5+(8a+8)x^4+x^3+(6a+7)x^2+(7a+8)x+2a+5$
- $y^2=6ax^6+(9a+9)x^5+(3a+6)x^4+8ax^2+(3a+10)x+2a+3$
- $y^2=(3a+5)x^6+(a+9)x^5+(5a+10)x^4+(8a+6)x^3+(4a+7)x^2+3x+3a+7$
- $y^2=(6a+4)x^6+(5a+6)x^5+(5a+5)x^4+10ax^3+(4a+9)x^2+(10a+8)x+10a+5$
- $y^2=(3a+7)x^6+(7a+10)x^5+(10a+2)x^4+2ax^3+(2a+10)x^2+(a+5)x+6a+5$
- $y^2=(9a+10)x^6+(8a+1)x^5+(10a+9)x^4+(7a+9)x^3+(10a+9)x^2+(8a+1)x+9a+10$
- $y^2=(8a+4)x^6+(2a+7)x^5+(2a+6)x^4+3x^3+4x^2+(7a+6)x+5a+6$
- $y^2=(2a+10)x^6+ax^5+(6a+3)x^4+(9a+4)x^3+(6a+6)x^2+(4a+8)x+2a+10$
- $y^2=(a+7)x^6+10x^5+(10a+2)x^4+(6a+7)x^3+(4a+4)x^2+(7a+3)x+a+5$
- $y^2=(a+6)x^6+(8a+8)x^5+(10a+5)x^4+2x^3+(9a+2)x^2+(9a+4)x+2a+10$
- $y^2=(7a+8)x^6+(2a+10)x^5+(6a+5)x^4+(7a+9)x^3+(6a+5)x^2+(2a+10)x+7a+8$
- $y^2=(2a+9)x^6+(4a+2)x^5+(4a+7)x^4+(2a+4)x^3+(4a+7)x^2+(4a+2)x+2a+9$
- $y^2=(2a+3)x^6+(6a+10)x^5+(7a+6)x^4+4ax^3+3x^2+(8a+5)x+3a+7$
- $y^2=9ax^6+(2a+1)x^5+(7a+9)x^4+4x^3+(2a+3)x^2+7x+5a+2$
- and 24 more
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{11^{2}}$.
Endomorphism algebra over $\F_{11^{2}}$The isogeny class factors as 1.121.av $\times$ 1.121.ap and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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 |
---|---|---|
2.121.ag_acv | $2$ | (not in LMFDB) |
2.121.g_acv | $2$ | (not in LMFDB) |
2.121.bk_vl | $2$ | (not in LMFDB) |