Invariants
Base field: | $\F_{97}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 19 x + 97 x^{2} )^{2}$ |
$1 - 38 x + 555 x^{2} - 3686 x^{3} + 9409 x^{4}$ | |
Frobenius angles: | $\pm0.0849741350078$, $\pm0.0849741350078$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $2$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $6241$ | $85433049$ | $830547886336$ | $7835827755484521$ | $73741668375066892561$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $60$ | $9076$ | $910014$ | $88511140$ | $8587253580$ | $832972117822$ | $80798295030828$ | $7837433783928004$ | $760231061232421758$ | $73742412720085649236$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=5x^6+5x^3+59$
- $y^2=15x^6+94x^5+20x^4+69x^3+90x^2+12x+21$
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 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$ |
Base change
This is a primitive isogeny class.