Invariants
| Base field: | $\F_{107}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 35 x + 519 x^{2} - 3745 x^{3} + 11449 x^{4}$ |
| Frobenius angles: | $\pm0.143612554606$, $\pm0.209116986977$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.324725.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $8189$ | $128968561$ | $1501204032431$ | $17185171795181021$ | $196720525798442713264$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $73$ | $11263$ | $1225429$ | $131104851$ | $14025901608$ | $1500734280907$ | $160578175862779$ | $17181861896789043$ | $1838459211537515443$ | $196715135707639475478$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=105x^6+2x^5+4x^4+58x^3+97x^2+100x+86$
- $y^2=99x^6+81x^5+13x^4+34x^3+59x^2+105x+5$
- $y^2=85x^6+97x^5+29x^4+87x^3+14x^2+40x+63$
- $y^2=57x^6+87x^5+53x^4+64x^3+11x^2+84x+80$
- $y^2=98x^6+27x^5+23x^4+106x^3+42x^2+82x+50$
- $y^2=88x^6+2x^5+42x^4+75x^3+93x^2+80x+104$
- $y^2=41x^6+28x^5+101x^4+85x^3+23x^2+71x+84$
- $y^2=28x^6+60x^5+63x^4+67x^3+89x^2+30x+65$
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 4.0.324725.1. |
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_tz | $2$ | (not in LMFDB) |