Invariants
| Base field: | $\F_{181}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 24 x + 181 x^{2} )( 1 - 23 x + 181 x^{2} )$ |
| $1 - 47 x + 914 x^{2} - 8507 x^{3} + 32761 x^{4}$ | |
| Frobenius angles: | $\pm0.149335043618$, $\pm0.173686936480$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $25122$ | $1060902060$ | $35159052952800$ | $1151998223159010240$ | $37738873490422887496362$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $135$ | $32381$ | $5929272$ | $1073340481$ | $194265668955$ | $35161851315098$ | $6364291209404655$ | $1151936660311275361$ | $208500535073951143992$ | $37738596846700652690501$ |
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 $\F_{181}$.
Endomorphism algebra over $\F_{181}$| The isogeny class factors as 1.181.ay $\times$ 1.181.ax 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 |
|---|---|---|
| 2.181.ab_ahi | $2$ | (not in LMFDB) |
| 2.181.b_ahi | $2$ | (not in LMFDB) |
| 2.181.bv_bje | $2$ | (not in LMFDB) |