Invariants
| Base field: | $\F_{97}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 18 x + 97 x^{2} )^{2}$ |
| $1 - 36 x + 518 x^{2} - 3492 x^{3} + 9409 x^{4}$ | |
| Frobenius angles: | $\pm0.133124938748$, $\pm0.133124938748$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $10$ |
This isogeny class is not 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $6400$ | $86118400$ | $831889926400$ | $7837773373440000$ | $73743995224569760000$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $62$ | $9150$ | $911486$ | $88533118$ | $8587524542$ | $832974949950$ | $80798319612926$ | $7837433941136638$ | $760231061488162622$ | $73742412706861890750$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=22x^6+92x^4+92x^2+22$
- $y^2=53x^6+66x^4+66x^2+53$
- $y^2=21x^6+32x^4+32x^2+21$
- $y^2=21x^6+45x^5+20x^4+95x^3+41x^2+23x+76$
- $y^2=10x^6+42x^5+18x^4+52x^3+72x^2+90x+58$
- $y^2=45x^6+34x^5+24x^4+64x^3+74x^2+46x+17$
- $y^2=39x^6+64x^5+81x^4+16x^3+35x^2+88x+82$
- $y^2=32x^6+96x^5+45x^4+5x^3+45x^2+96x+32$
- $y^2=56x^6+56x^5+84x^4+29x^3+84x^2+56x+56$
- $y^2=69x^6+24x^5+20x^4+94x^3+20x^2+24x+69$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{97}$.
Endomorphism algebra over $\F_{97}$| The isogeny class factors as 1.97.as 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-1}) \)$)$ |
Base change
This is a primitive isogeny class.