Invariants
| Base field: | $\F_{181}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 26 x + 181 x^{2} )( 1 - 24 x + 181 x^{2} )$ |
| $1 - 50 x + 986 x^{2} - 9050 x^{3} + 32761 x^{4}$ | |
| Frobenius angles: | $\pm0.0828936782352$, $\pm0.149335043618$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $8$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $24648$ | $1056117504$ | $35136641521800$ | $1151922333134536704$ | $37738671201839627609928$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $132$ | $32234$ | $5925492$ | $1073269774$ | $194264627652$ | $35161839461018$ | $6364291124941812$ | $1151936660633628574$ | $208500535099811072772$ | $37738596847297580676554$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=19x^6+94x^5+110x^4+130x^3+77x^2+180x+141$
- $y^2=57x^6+49x^5+180x^4+138x^3+180x^2+49x+57$
- $y^2=62x^6+20x^5+68x^4+26x^3+53x^2+136x+39$
- $y^2=90x^6+4x^5+179x^4+70x^3+88x^2+142x+57$
- $y^2=96x^6+77x^5+109x^4+22x^3+109x^2+77x+96$
- $y^2=35x^6+96x^5+34x^4+22x^3+73x^2+58x+22$
- $y^2=66x^6+175x^5+107x^4+73x^3+107x^2+175x+66$
- $y^2=81x^6+140x^5+54x^4+x^3+54x^2+140x+81$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{181}$.
Endomorphism algebra over $\F_{181}$| The isogeny class factors as 1.181.aba $\times$ 1.181.ay 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.