Invariants
| Base field: | $\F_{47}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 92 x^{2} + 2209 x^{4}$ |
| Frobenius angles: | $\pm0.0328896496719$, $\pm0.967110350328$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-2}, \sqrt{-93})\) |
| Galois group: | $C_2^2$ |
| Jacobians: | $0$ |
| Cyclic group of points: | yes |
This isogeny class is simple but not geometrically 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $2118$ | $4485924$ | $10779046326$ | $23771826404496$ | $52599132000970518$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $48$ | $2026$ | $103824$ | $4871590$ | $229345008$ | $10778877322$ | $506623120464$ | $23811273440254$ | $1119130473102768$ | $52599131766110986$ |
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 $\F_{47^{2}}$.
Endomorphism algebra over $\F_{47}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-2}, \sqrt{-93})\). |
| The base change of $A$ to $\F_{47^{2}}$ is 1.2209.ado 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-93}) \)$)$ |
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 |
|---|---|---|
| 2.47.a_do | $4$ | (not in LMFDB) |
| 2.47.ac_c | $8$ | (not in LMFDB) |
| 2.47.c_c | $8$ | (not in LMFDB) |