Invariants
| Base field: | $\F_{29}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 + 10 x + 29 x^{2}$ |
| Frobenius angles: | $\pm0.878881058409$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-1}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $2$ |
| Isomorphism classes: | 2 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $40$ | $800$ | $24520$ | $707200$ | $20508200$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $40$ | $800$ | $24520$ | $707200$ | $20508200$ | $594855200$ | $17249643080$ | $500247820800$ | $14507138661160$ | $420707265620000$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 2 curves (of which 0 are hyperelliptic):
- $y^2=x^3+12 x+12$
- $y^2=x^3+4 x$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{29}$.
Endomorphism algebra over $\F_{29}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-1}) \). |
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 |
|---|---|---|
| 1.29.ak | $2$ | (not in LMFDB) |
| 1.29.ae | $4$ | (not in LMFDB) |
| 1.29.e | $4$ | (not in LMFDB) |