Invariants
| Base field: | $\F_{83}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 30 x + 384 x^{2} - 2490 x^{3} + 6889 x^{4}$ |
| Frobenius angles: | $\pm0.0801876089965$, $\pm0.262835026667$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.2900800.5 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4754$ | $46560676$ | $326991667466$ | $2252588556793936$ | $15516162317924403914$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $54$ | $6758$ | $571878$ | $47464566$ | $3939071394$ | $326940031622$ | $27136043856738$ | $2252292182936158$ | $186940255467694374$ | $15516041196697785878$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=55x^6+15x^5+80x^4+40x^3+13x^2+56x+64$
- $y^2=22x^6+10x^5+11x^4+25x^3+14x^2+29x+31$
- $y^2=67x^6+70x^5+14x^4+42x^3+39x+27$
- $y^2=56x^6+16x^5+13x^4+12x^3+40x^2+49$
- $y^2=77x^6+17x^5+59x^4+4x^3+77x^2+26x+62$
- $y^2=17x^6+69x^5+59x^4+6x^3+78x^2+51x+6$
- $y^2=58x^6+3x^5+59x^4+77x^3+80x^2+49x+8$
- $y^2=50x^6+26x^5+71x^4+14x^3+31x^2+22x+48$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{83}$.
Endomorphism algebra over $\F_{83}$| The endomorphism algebra of this simple isogeny class is 4.0.2900800.5. |
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 |
|---|---|---|
| 2.83.be_ou | $2$ | (not in LMFDB) |