Invariants
| Base field: | $\F_{11^{2}}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 38 x + 600 x^{2} - 4598 x^{3} + 14641 x^{4}$ |
| Frobenius angles: | $\pm0.108595780943$, $\pm0.212710791608$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.1449792.4 |
| Galois group: | $D_{4}$ |
| Jacobians: | $20$ |
| Isomorphism classes: | 20 |
This isogeny class is simple and geometrically 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $10606$ | $210826068$ | $3137959133854$ | $45954045608716752$ | $672759308141675840206$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $84$ | $14398$ | $1771296$ | $214379014$ | $25937783664$ | $3138432291214$ | $379749863358180$ | $45949730002539070$ | $5559917313649818660$ | $672749994934761264718$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=2ax^6+(3a+1)x^5+(7a+8)x^4+(9a+1)x^3+(9a+6)x^2+(5a+1)x+5a+5$
- $y^2=2ax^6+(4a+7)x^5+(7a+10)x^4+(4a+5)x^3+7x^2+(4a+3)x+2a+2$
- $y^2=(5a+5)x^6+(7a+10)x^5+(8a+2)x^4+(a+9)x^3+(10a+3)x^2+(6a+7)x+10a+6$
- $y^2=(7a+2)x^6+(7a+9)x^5+(5a+1)x^4+(5a+9)x^3+(4a+7)x^2+(6a+7)x+a+7$
- $y^2=3ax^6+(10a+8)x^5+(2a+8)x^4+(9a+8)x^3+(8a+10)x^2+(9a+3)x+4a+1$
- $y^2=(4a+5)x^6+3x^5+(a+8)x^4+(5a+3)x^3+(3a+2)x^2+(5a+6)x+10a+7$
- $y^2=(9a+6)x^6+(6a+10)x^4+6ax^3+(5a+6)x^2+3ax+6a+6$
- $y^2=(9a+6)x^6+(a+6)x^5+(4a+6)x^4+(a+5)x^3+(5a+4)x^2+(6a+3)x+6a+1$
- $y^2=(5a+3)x^6+4x^5+(8a+4)x^4+(3a+1)x^3+(10a+8)x^2+10ax+3a+10$
- $y^2=(2a+7)x^6+(10a+8)x^5+(9a+9)x^4+(2a+2)x^3+(2a+7)x^2+(2a+10)x+4a+7$
- $y^2=(9a+8)x^6+(a+4)x^5+3ax^4+(a+1)x^3+(5a+8)x^2+(3a+10)x+9a+10$
- $y^2=(6a+4)x^6+(10a+5)x^5+7x^4+(4a+5)x^3+(3a+4)x^2+(4a+3)x+2a+3$
- $y^2=5ax^6+(4a+4)x^5+(8a+7)x^4+(7a+10)x^3+(2a+5)x^2+(4a+10)x+a$
- $y^2=(3a+7)x^6+(6a+8)x^5+(4a+2)x^4+(6a+6)x^3+10ax^2+(2a+1)x+5a+6$
- $y^2=(2a+4)x^6+(6a+9)x^5+(6a+1)x^4+(7a+2)x^3+(9a+9)x^2+(4a+1)x+5a+2$
- $y^2=(2a+6)x^6+(10a+3)x^5+(7a+9)x^4+2ax^3+(7a+3)x^2+5x+7a+1$
- $y^2=(9a+8)x^6+(a+5)x^5+9ax^4+(10a+1)x^3+(6a+9)x^2+(6a+1)x+9a+1$
- $y^2=(4a+2)x^6+(7a+1)x^5+(8a+8)x^4+(6a+10)x^3+(5a+5)x^2+(2a+2)x+5a+7$
- $y^2=(7a+7)x^6+(5a+2)x^5+(9a+3)x^4+(8a+5)x^3+(3a+7)x^2+(a+8)x+9$
- $y^2=(8a+2)x^6+(10a+9)x^5+(7a+8)x^4+(3a+9)x^3+(6a+6)x^2+(2a+7)x+5a+2$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{11^{2}}$.
Endomorphism algebra over $\F_{11^{2}}$| The endomorphism algebra of this simple isogeny class is 4.0.1449792.4. |
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.bm_xc | $2$ | (not in LMFDB) |