Invariants
Base field: | $\F_{79}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 27 x + 323 x^{2} - 2133 x^{3} + 6241 x^{4}$ |
Frobenius angles: | $\pm0.0374785281705$, $\pm0.323768918442$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.4746717.1 |
Galois group: | $D_{4}$ |
Jacobians: | $6$ |
Isomorphism classes: | 6 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4405$ | $38433625$ | $243126534955$ | $1516967376724125$ | $9467867668664508400$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $53$ | $6159$ | $493121$ | $38946451$ | $3076923668$ | $243085735347$ | $19203897163427$ | $1517108785853011$ | $119851596311162339$ | $9468276084784555374$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=41x^6+48x^5+56x^4+59x^3+28x^2+68x+19$
- $y^2=61x^6+41x^5+56x^4+37x^3+47x^2+11x+7$
- $y^2=15x^6+22x^5+16x^4+14x^3+24x^2+78x+30$
- $y^2=54x^6+69x^5+27x^4+35x^3+40x^2+35x+52$
- $y^2=57x^6+10x^5+64x^4+7x^3+48x^2+49x+41$
- $y^2=13x^6+14x^5+71x^4+14x^3+9x^2+64x+17$
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 4.0.4746717.1. |
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.bb_ml | $2$ | (not in LMFDB) |