Invariants
| Base field: | $\F_{97}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 19 x + 97 x^{2} )( 1 - 15 x + 97 x^{2} )$ |
| $1 - 34 x + 479 x^{2} - 3298 x^{3} + 9409 x^{4}$ | |
| Frobenius angles: | $\pm0.0849741350078$, $\pm0.224458531442$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $8$ |
| Isomorphism classes: | 14 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $6557$ | $86690097$ | $832662204416$ | $7838211427726329$ | $73743516052221172277$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $64$ | $9212$ | $912334$ | $88538068$ | $8587468744$ | $832972906622$ | $80798285766136$ | $7837433547338596$ | $760231058203153678$ | $73742412692440087532$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=64x^6+91x^5+2x^4+2x^3+79x^2+38x+35$
- $y^2=43x^6+2x^5+83x^4+57x^3+26x^2+67x+58$
- $y^2=82x^6+79x^5+8x^4+69x^3+96x^2+27x+76$
- $y^2=19x^6+94x^5+29x^4+69x^3+40x^2+53x+51$
- $y^2=6x^6+24x^5+81x^4+17x^3+46x^2+96x+30$
- $y^2=22x^6+84x^5+85x^4+46x^3+42x^2+20x+38$
- $y^2=71x^6+20x^5+3x^4+17x^3+31x^2+77x+10$
- $y^2=10x^6+42x^5+40x^4+74x^3+77x^2+59x+23$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{97}$.
Endomorphism algebra over $\F_{97}$| The isogeny class factors as 1.97.at $\times$ 1.97.ap and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
Base change
This is a primitive isogeny class.