Invariants
| Base field: | $\F_{79}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 31 x + 395 x^{2} - 2449 x^{3} + 6241 x^{4}$ |
| Frobenius angles: | $\pm0.0736417724422$, $\pm0.219992096097$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.40053.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $8$ |
| Isomorphism classes: | 8 |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
| $p$-rank: | $1$ |
| Slopes: | $[0, 1/2, 1/2, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4157$ | $37899369$ | $242889016283$ | $1517268379162077$ | $9468463427573309072$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $49$ | $6071$ | $492637$ | $38954179$ | $3077117284$ | $243087804875$ | $19203908315599$ | $1517108774660275$ | $119851595630443471$ | $9468276081809194286$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=26x^6+42x^5+53x^4+62x^3+49x^2+72x+35$
- $y^2=57x^6+7x^5+33x^4+61x^3+51x^2+12x+53$
- $y^2=30x^6+69x^5+68x^3+70x^2+60x+25$
- $y^2=66x^6+71x^5+27x^4+12x^3+17x^2+71x+48$
- $y^2=58x^6+10x^5+19x^4+59x^3+60x^2+15x+15$
- $y^2=49x^6+39x^5+23x^4+10x^3+34x^2+21x+25$
- $y^2=57x^6+34x^5+7x^4+29x^3+33x^2+4x+3$
- $y^2=10x^6+73x^5+66x^4+9x^3+52x^2+49x+20$
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 4.0.40053.1. |
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.bf_pf | $2$ | (not in LMFDB) |