Invariants
| Base field: | $\F_{47}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 21 x + 200 x^{2} - 987 x^{3} + 2209 x^{4}$ |
| Frobenius angles: | $\pm0.131283800781$, $\pm0.288979548104$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.1019592.3 |
| Galois group: | $D_{4}$ |
| Jacobians: | $8$ |
| Isomorphism classes: | 8 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1402$ | $4792036$ | $10818544216$ | $23832021789216$ | $52603607060842702$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $27$ | $2169$ | $104202$ | $4883929$ | $229364517$ | $10779239274$ | $506623078275$ | $23811290860753$ | $1119130550256726$ | $52599132921732129$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which all are hyperelliptic):
- $y^2=21 x^6+30 x^5+35 x^4+36 x^3+20 x^2+16 x+12$
- $y^2=12 x^6+16 x^5+13 x^4+8 x^3+41 x^2+12 x+38$
- $y^2=35 x^6+46 x^5+33 x^4+27 x^3+34 x^2+4 x+5$
- $y^2=18 x^5+31 x^4+32 x^3+28 x^2+17 x+14$
- $y^2=9 x^6+32 x^5+33 x^4+41 x^3+33 x^2+15 x+23$
- $y^2=24 x^6+14 x^5+13 x^4+39 x^3+45 x^2+22 x+6$
- $y^2=30 x^6+x^5+23 x^4+27 x^3+5 x^2+13 x+10$
- $y^2=16 x^6+10 x^5+5 x^4+27 x^3+37 x^2+33 x+5$
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 4.0.1019592.3. |
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.v_hs | $2$ | (not in LMFDB) |