Invariants
| Base field: | $\F_{97}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 17 x + 97 x^{2} )( 1 - 16 x + 97 x^{2} )$ |
| $1 - 33 x + 466 x^{2} - 3201 x^{3} + 9409 x^{4}$ | |
| Frobenius angles: | $\pm0.168554845458$, $\pm0.198227810371$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 12 |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $6642$ | $87076620$ | $833515977672$ | $7839626522803200$ | $73745404969850321202$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $65$ | $9253$ | $913268$ | $88554049$ | $8587688705$ | $832975340866$ | $80798305877921$ | $7837433628370561$ | $760231057203837236$ | $73742412662890745893$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{97}$.
Endomorphism algebra over $\F_{97}$| The isogeny class factors as 1.97.ar $\times$ 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.
Twists
Below is a list of all twists of this isogeny class.
| Twist | Extension degree | Common base change |
|---|---|---|
| 2.97.ab_ada | $2$ | (not in LMFDB) |
| 2.97.b_ada | $2$ | (not in LMFDB) |
| 2.97.bh_ry | $2$ | (not in LMFDB) |