Invariants
| Base field: | $\F_{79}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 30 x + 381 x^{2} - 2370 x^{3} + 6241 x^{4}$ |
| Frobenius angles: | $\pm0.125421770554$, $\pm0.223104329322$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.391744.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $7$ |
| Isomorphism classes: | 7 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4223$ | $38104129$ | $243176809700$ | $1517570135456809$ | $9468727958986983503$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $50$ | $6104$ | $493220$ | $38961924$ | $3077203250$ | $243088637078$ | $19203915425150$ | $1517108827032004$ | $119851595926923260$ | $9468276082317517304$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 7 curves (of which all are hyperelliptic):
- $y^2=x^6+42 x^5+3 x^4+37 x^3+18 x^2+20 x+62$
- $y^2=3 x^6+36 x^5+52 x^4+68 x^3+71 x^2+44 x+58$
- $y^2=75 x^6+54 x^5+62 x^4+55 x^3+3 x^2+x+48$
- $y^2=22 x^6+43 x^5+45 x^4+59 x^3+14 x^2+9 x+41$
- $y^2=58 x^6+25 x^5+12 x^4+47 x^3+72 x^2+46 x+47$
- $y^2=28 x^6+2 x^5+58 x^4+72 x^3+73 x^2+37 x+28$
- $y^2=19 x^6+45 x^5+54 x^4+44 x^3+34 x^2+10 x+48$
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 4.0.391744.1. |
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 |
|---|---|---|
| 2.79.be_or | $2$ | (not in LMFDB) |