Invariants
| Base field: | $\F_{47}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 19 x + 170 x^{2} - 893 x^{3} + 2209 x^{4}$ |
| Frobenius angles: | $\pm0.0805235083544$, $\pm0.362890760758$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.1484793.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $8$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1468$ | $4832656$ | $10794914512$ | $23803131144256$ | $52591241392814308$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $29$ | $2189$ | $103976$ | $4878009$ | $229310599$ | $10779028094$ | $506623582753$ | $23811300243793$ | $1119130561379960$ | $52599132430579829$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which all are hyperelliptic):
- $y^2=4 x^6+34 x^5+40 x^4+36 x^3+36 x^2+17 x+37$
- $y^2=21 x^6+18 x^5+29 x^4+5 x^3+3 x^2+45 x+34$
- $y^2=46 x^6+5 x^5+13 x^4+16 x^3+24 x^2+13 x$
- $y^2=33 x^6+38 x^5+35 x^4+15 x^3+36 x^2+43 x+2$
- $y^2=18 x^6+42 x^5+23 x^4+39 x^3+23 x^2+44 x+19$
- $y^2=4 x^6+24 x^5+6 x^4+19 x^3+4 x^2+30 x+12$
- $y^2=34 x^6+22 x^5+40 x^4+9 x^3+13 x^2+35 x+10$
- $y^2=3 x^6+27 x^5+9 x^4+45 x^3+25 x^2+46 x+26$
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 4.0.1484793.1. |
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.t_go | $2$ | (not in LMFDB) |