Invariants
| Base field: | $\F_{47}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 13 x + 47 x^{2} )( 1 - 12 x + 47 x^{2} )$ |
| $1 - 25 x + 250 x^{2} - 1175 x^{3} + 2209 x^{4}$ | |
| Frobenius angles: | $\pm0.102979434792$, $\pm0.160736311100$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
This isogeny class is not 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1260$ | $4611600$ | $10737906480$ | $23814763560000$ | $52605124367865300$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $23$ | $2085$ | $103424$ | $4880393$ | $229371133$ | $10779496830$ | $506625345739$ | $23811301044913$ | $1119130549415168$ | $52599132540716925$ |
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 $\F_{47}$.
Endomorphism algebra over $\F_{47}$| The isogeny class factors as 1.47.an $\times$ 1.47.am and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.ab_ack | $2$ | (not in LMFDB) |
| 2.47.b_ack | $2$ | (not in LMFDB) |
| 2.47.z_jq | $2$ | (not in LMFDB) |