Invariants
| Base field: | $\F_{107}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 35 x + 512 x^{2} - 3745 x^{3} + 11449 x^{4}$ |
| Frobenius angles: | $\pm0.0556953677470$, $\pm0.250022197142$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.3023064.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $8182$ | $128801044$ | $1500301037464$ | $17182567260917536$ | $196715354179015825882$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $73$ | $11249$ | $1224694$ | $131084985$ | $14025532883$ | $1500729131378$ | $160578121123409$ | $17181861491544049$ | $1838459210514549058$ | $196715135733968394689$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=2x^6+4x^5+36x^4+76x^3+26x^2+15x+98$
- $y^2=75x^6+92x^5+58x^4+50x^3+14x^2+9x+38$
- $y^2=21x^6+51x^5+15x^4+92x^3+65x^2+87x+55$
- $y^2=93x^6+88x^5+95x^4+14x^3+55x^2+9x+53$
- $y^2=65x^6+102x^5+51x^4+x^3+98x^2+30x+86$
- $y^2=47x^6+26x^5+59x^4+50x^3+51x^2+63x+15$
- $y^2=63x^6+87x^5+66x^4+46x^3+93x^2+65x+95$
- $y^2=91x^6+59x^5+41x^4+44x^3+9x^2+96x+7$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{107}$.
Endomorphism algebra over $\F_{107}$| The endomorphism algebra of this simple isogeny class is 4.0.3023064.1. |
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 |
|---|---|---|
| 2.107.bj_ts | $2$ | (not in LMFDB) |