Invariants
| Base field: | $\F_{47}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 8 x + 47 x^{2} )( 1 - 7 x + 47 x^{2} )$ |
| $1 - 15 x + 150 x^{2} - 705 x^{3} + 2209 x^{4}$ | |
| Frobenius angles: | $\pm0.301698511018$, $\pm0.329450163008$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Cyclic group of points: | no |
| Non-cyclic primes: | $2$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1640$ | $5051200$ | $10910637920$ | $23840148640000$ | $52595847338202200$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $33$ | $2285$ | $105084$ | $4885593$ | $229330683$ | $10778836430$ | $506620969629$ | $23811288077713$ | $1119130581486708$ | $52599132969847925$ |
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.ai $\times$ 1.47.ah 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_bm | $2$ | (not in LMFDB) |
| 2.47.b_bm | $2$ | (not in LMFDB) |
| 2.47.p_fu | $2$ | (not in LMFDB) |