Invariants
| Base field: | $\F_{97}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 31 x + 417 x^{2} - 3007 x^{3} + 9409 x^{4}$ |
| Frobenius angles: | $\pm0.0213770737388$, $\pm0.304596925309$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.2156733.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $8$ |
| Isomorphism classes: | 8 |
This isogeny class is simple and geometrically 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $6789$ | $87340485$ | $832942090917$ | $7837116306853125$ | $73740795231945621504$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $67$ | $9283$ | $912643$ | $88525699$ | $8587151902$ | $832968761731$ | $80798252000995$ | $7837433407326211$ | $760231058418892771$ | $73742412693043705918$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=36x^6+65x^5+76x^4+77x^3+9x^2+33x+5$
- $y^2=41x^6+24x^5+68x^4+87x^3+27x^2+29x+91$
- $y^2=40x^6+67x^5+61x^4+9x^3+95x^2+21x+80$
- $y^2=46x^6+34x^5+34x^4+93x^3+70x^2+69x+63$
- $y^2=27x^6+32x^5+49x^4+24x^3+71x^2+5x+16$
- $y^2=80x^6+91x^5+2x^4+15x^3+15x^2+18x+58$
- $y^2=76x^6+33x^5+25x^4+40x^3+7x^2+66x+29$
- $y^2=84x^6+37x^5+36x^4+84x^3+20x+26$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{97}$.
Endomorphism algebra over $\F_{97}$| The endomorphism algebra of this simple isogeny class is 4.0.2156733.1. |
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.bf_qb | $2$ | (not in LMFDB) |