Invariants
| Base field: | $\F_{79}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 29 x + 360 x^{2} - 2291 x^{3} + 6241 x^{4}$ |
| Frobenius angles: | $\pm0.0680014220525$, $\pm0.273043216394$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.2796552.2 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4282$ | $38204004$ | $243115705528$ | $1517255514730272$ | $9468251903758392622$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $51$ | $6121$ | $493098$ | $38953849$ | $3077048541$ | $243086759530$ | $19203899899851$ | $1517108755445905$ | $119851596128860854$ | $9468276090000669361$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=37x^6+54x^5+50x^4+64x^3+67x^2+42x+36$
- $y^2=16x^6+59x^5+76x^4+73x^3+30x^2+26x+75$
- $y^2=64x^6+15x^5+69x^4+37x^3+28x^2+6x+55$
- $y^2=7x^6+44x^5+60x^4+51x^3+25x^2+42x+42$
- $y^2=78x^6+42x^5+5x^4+35x^3+54x^2+78x+77$
- $y^2=15x^6+56x^5+9x^4+27x^3+14x^2+68x+15$
- $y^2=41x^6+4x^5+69x^4+4x^3+71x^2+21x+35$
- $y^2=75x^6+7x^5+75x^4+56x^3+14x^2+75x+38$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{79}$.
Endomorphism algebra over $\F_{79}$| The endomorphism algebra of this simple isogeny class is 4.0.2796552.2. |
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 |
|---|---|---|
| 2.79.bd_nw | $2$ | (not in LMFDB) |