Invariants
| Base field: | $\F_{151}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 23 x + 151 x^{2} )( 1 - 21 x + 151 x^{2} )$ |
| $1 - 44 x + 785 x^{2} - 6644 x^{3} + 22801 x^{4}$ | |
| Frobenius angles: | $\pm0.114627783796$, $\pm0.173877215616$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $7$ |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $16899$ | $511617225$ | $11848767377616$ | $270291620762678025$ | $6162728308173809461779$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $108$ | $22436$ | $3441456$ | $519905956$ | $78503367228$ | $11853922241198$ | $1789940784355188$ | $270281039480853316$ | $40812436767323757456$ | $6162677950370399971076$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 7 curves (of which all are hyperelliptic):
- $y^2=33 x^6+72 x^5+81 x^4+25 x^3+25 x^2+40 x+33$
- $y^2=70 x^6+29 x^5+20 x^4+114 x^3+55 x^2+40 x+26$
- $y^2=140 x^6+124 x^5+86 x^4+138 x^3+49 x^2+16 x+146$
- $y^2=119 x^6+139 x^5+59 x^4+33 x^3+137 x^2+8 x+12$
- $y^2=134 x^6+65 x^5+9 x^4+121 x^3+85 x^2+140 x+133$
- $y^2=23 x^6+125 x^5+25 x^4+92 x^3+40 x^2+18 x+93$
- $y^2=15 x^6+105 x^5+7 x^4+120 x^3+92 x^2+125 x+133$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{151}$.
Endomorphism algebra over $\F_{151}$| The isogeny class factors as 1.151.ax $\times$ 1.151.av 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.