Invariants
| Base field: | $\F_{107}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 37 x + 555 x^{2} - 3959 x^{3} + 11449 x^{4}$ |
| Frobenius angles: | $\pm0.102828115080$, $\pm0.182443960365$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.135725.2 |
| Galois group: | $D_{4}$ |
| Jacobians: | $4$ |
| Isomorphism classes: | 4 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $8009$ | $128152009$ | $1499599225331$ | $17183019791315981$ | $196718479835445595984$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $71$ | $11191$ | $1224119$ | $131088435$ | $14025755736$ | $1500733574587$ | $160578180121745$ | $17181862054041939$ | $1838459213887934333$ | $196715135733005324886$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=41x^6+26x^5+86x^4+25x^3+104x^2+30x+9$
- $y^2=77x^6+106x^5+64x^4+40x^3+95x^2+82x+54$
- $y^2=93x^6+103x^5+59x^4+7x^3+71x^2+16x+25$
- $y^2=51x^6+4x^5+46x^4+31x^3+12x^2+87x+71$
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 4.0.135725.2. |
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.bl_vj | $2$ | (not in LMFDB) |