Invariants
| Base field: | $\F_{97}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - 2 x + 97 x^{2}$ |
| Frobenius angles: | $\pm0.467624736821$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-6}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $14$ |
| Isomorphism classes: | 14 |
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: | $1$ |
| Slopes: | $[0, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $96$ | $9600$ | $913248$ | $88512000$ | $8587250016$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $96$ | $9600$ | $913248$ | $88512000$ | $8587250016$ | $832973500800$ | $80798296223328$ | $7837433472768000$ | $760231057272061536$ | $73742412698523888000$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 14 curves (of which 0 are hyperelliptic):
- $y^2=x^3+33 x+68$
- $y^2=x^3+69 x+54$
- $y^2=x^3+36 x+36$
- $y^2=x^3+14 x+70$
- $y^2=x^3+3 x+3$
- $y^2=x^3+25 x+25$
- $y^2=x^3+56 x+56$
- $y^2=x^3+40 x+40$
- $y^2=x^3+35 x+78$
- $y^2=x^3+71 x+64$
- $y^2=x^3+18 x+18$
- $y^2=x^3+73 x+74$
- $y^2=x^3+48 x+48$
- $y^2=x^3+2 x+10$
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 \(\Q(\sqrt{-6}) \). |
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 |
|---|---|---|
| 1.97.c | $2$ | (not in LMFDB) |