Invariants
| Base field: | $\F_{193}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 27 x + 193 x^{2} )( 1 - 26 x + 193 x^{2} )$ |
| $1 - 53 x + 1088 x^{2} - 10229 x^{3} + 37249 x^{4}$ | |
| Frobenius angles: | $\pm0.0758389534121$, $\pm0.114714697559$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $28056$ | $1364082720$ | $51635318652288$ | $1925049761953718400$ | $71708865687914240527896$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $141$ | $36617$ | $7182486$ | $1387435249$ | $267785037861$ | $51682546542494$ | $9974730508047285$ | $1925122956514720801$ | $371548729972630550358$ | $71708904874146847968857$ |
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 $\F_{193}$.
Endomorphism algebra over $\F_{193}$| The isogeny class factors as 1.193.abb $\times$ 1.193.aba 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 |
|---|---|---|
| 2.193.ab_ame | $2$ | (not in LMFDB) |
| 2.193.b_ame | $2$ | (not in LMFDB) |
| 2.193.cb_bpw | $2$ | (not in LMFDB) |