Invariants
Base field: | $\F_{97}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 18 x + 97 x^{2} )( 1 - 16 x + 97 x^{2} )$ |
$1 - 34 x + 482 x^{2} - 3298 x^{3} + 9409 x^{4}$ | |
Frobenius angles: | $\pm0.133124938748$, $\pm0.198227810371$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $16$ |
Isomorphism classes: | 60 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $6560$ | $86749440$ | $832942466720$ | $7838929236787200$ | $73744794903449712800$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $64$ | $9218$ | $912640$ | $88546174$ | $8587617664$ | $832974989186$ | $80798308262848$ | $7837433720594686$ | $760231058713689280$ | $73742412681029289218$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=93x^6+84x^5+73x^4+18x^3+88x^2+30x+93$
- $y^2=23x^6+17x^5+48x^4+18x^3+4x^2+21x+58$
- $y^2=36x^6+41x^5+85x^4+32x^3+50x^2+84x+31$
- $y^2=54x^6+84x^5+74x^4+58x^3+46x^2+45x+53$
- $y^2=57x^6+56x^5+58x^4+20x^3+58x^2+56x+57$
- $y^2=83x^6+94x^5+71x^4+67x^3+84x^2+72x+71$
- $y^2=26x^6+69x^5+6x^4+46x^3+6x^2+69x+26$
- $y^2=43x^6+23x^5+24x^4+62x^3+86x^2+5x+95$
- $y^2=60x^6+73x^5+36x^4+24x^3+36x^2+73x+60$
- $y^2=44x^6+16x^5+26x^4+73x^3+26x^2+16x+44$
- $y^2=90x^6+11x^5+30x^4+49x^3+30x^2+11x+90$
- $y^2=14x^6+85x^5+59x^4+88x^3+59x^2+85x+14$
- $y^2=75x^6+62x^5+51x^4+29x^3+58x^2+96x+22$
- $y^2=38x^6+14x^5+91x^4+68x^3+91x^2+14x+38$
- $y^2=36x^6+67x^5+55x^4+45x^3+87x^2+92x+43$
- $y^2=70x^6+46x^5+43x^4+74x^3+43x^2+46x+70$
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 $\times$ 1.97.aq 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.