Invariants
| Base field: | $\F_{47}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 22 x + 212 x^{2} - 1034 x^{3} + 2209 x^{4}$ |
| Frobenius angles: | $\pm0.121030160018$, $\pm0.263740142014$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.380736.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $6$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1366$ | $4750948$ | $10804411150$ | $23831458308304$ | $52605132061707646$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $26$ | $2150$ | $104066$ | $4883814$ | $229371166$ | $10779297590$ | $506623122598$ | $23811287189374$ | $1119130511531642$ | $52599132789905750$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 6 curves (of which all are hyperelliptic):
- $y^2=23 x^6+29 x^5+8 x^4+45 x^3+35 x^2+7 x+35$
- $y^2=5 x^6+45 x^5+3 x^4+27 x^3+30 x^2+30 x+40$
- $y^2=22 x^6+9 x^5+x^4+29 x^3+2 x^2+33 x+39$
- $y^2=40 x^6+31 x^5+12 x^4+30 x^2+7 x+29$
- $y^2=32 x^6+3 x^5+35 x^4+27 x^3+46 x^2+34 x+27$
- $y^2=31 x^6+26 x^5+32 x^4+13 x^3+31 x^2+15 x+26$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{47}$.
Endomorphism algebra over $\F_{47}$| The endomorphism algebra of this simple isogeny class is 4.0.380736.1. |
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 |
|---|---|---|
| 2.47.w_ie | $2$ | (not in LMFDB) |