Invariants
| Base field: | $\F_{73}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 26 x + 301 x^{2} - 1898 x^{3} + 5329 x^{4}$ |
| Frobenius angles: | $\pm0.0641967969525$, $\pm0.317741683996$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.7579712.2 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $3707$ | $28006385$ | $151414654028$ | $806450157511625$ | $4297473244558291347$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $48$ | $5256$ | $389226$ | $28397892$ | $2072997988$ | $151333207014$ | $11047392400596$ | $806460101776068$ | $58871587264529178$ | $4297625835010677736$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=17x^6+65x^5+27x^4+58x^3+38x^2+56x+45$
- $y^2=52x^6+36x^5+72x^4+29x^3+31x^2+11x+15$
- $y^2=6x^6+41x^5+72x^4+39x^3+31x^2+71x+4$
- $y^2=26x^6+34x^5+3x^4+14x^3+44x+4$
- $y^2=70x^6+36x^5+72x^4+32x^3+70x^2+30x+19$
- $y^2=34x^6+37x^5+3x^4+49x^3+28x^2+21x+31$
- $y^2=22x^6+30x^5+49x^4+28x^3+16x^2+24x+38$
- $y^2=25x^6+21x^5+58x^4+65x^3+52x^2+59x+45$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{73}$.
Endomorphism algebra over $\F_{73}$| The endomorphism algebra of this simple isogeny class is 4.0.7579712.2. |
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 |
|---|---|---|
| 2.73.ba_lp | $2$ | (not in LMFDB) |