Invariants
| Base field: | $\F_{373}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - 34 x + 373 x^{2}$ |
| Frobenius angles: | $\pm0.157390476300$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-21}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $12$ |
| Isomorphism classes: | 12 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $340$ | $138720$ | $51893860$ | $19356988800$ | $7220119947700$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $340$ | $138720$ | $51893860$ | $19356988800$ | $7220119947700$ | $2693103270651360$ | $1004527483732508740$ | $374688750748980979200$ | $139758904019649809872660$ | $52130071199253746143077600$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 12 curves (of which 0 are hyperelliptic):
- $y^2=x^3+6 x+12$
- $y^2=x^3+326 x+279$
- $y^2=x^3+122 x+122$
- $y^2=x^3+369 x+365$
- $y^2=x^3+182 x+182$
- $y^2=x^3+33 x+66$
- $y^2=x^3+30 x+30$
- $y^2=x^3+68 x+68$
- $y^2=x^3+207 x+41$
- $y^2=x^3+41 x+41$
- $y^2=x^3+225 x+225$
- $y^2=x^3+208 x+43$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{373}$.
Endomorphism algebra over $\F_{373}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-21}) \). |
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 |
|---|---|---|
| 1.373.bi | $2$ | (not in LMFDB) |