Invariants
| Base field: | $\F_{79}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 30 x + 380 x^{2} - 2370 x^{3} + 6241 x^{4}$ |
| Frobenius angles: | $\pm0.109651193138$, $\pm0.231789961120$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.726336.3 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4222$ | $38090884$ | $243132233782$ | $1517489167321296$ | $9468627336400840102$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $50$ | $6102$ | $493130$ | $38959846$ | $3077170550$ | $243088256742$ | $19203912224750$ | $1517108812199038$ | $119851596007209650$ | $9468276085168490502$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=24x^6+53x^5+25x^4+44x^3+46x^2+30x+43$
- $y^2=62x^6+62x^5+68x^4+2x^3+30x^2+52x+60$
- $y^2=39x^6+76x^5+42x^4+14x^3+64x^2+33x+26$
- $y^2=60x^6+72x^5+67x^4+60x^3+3x^2+3x+19$
- $y^2=7x^6+17x^5+66x^4+20x^3+74x^2+5x+6$
- $y^2=18x^6+35x^5+77x^4+36x^3+49x^2+74x+38$
- $y^2=9x^6+74x^5+76x^4+46x^3+27x^2+9x+54$
- $y^2=32x^6+78x^5+62x^4+19x^3+17x^2+53x$
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 4.0.726336.3. |
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.be_oq | $2$ | (not in LMFDB) |