Invariants
| Base field: | $\F_{199}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 27 x + 199 x^{2} )( 1 - 26 x + 199 x^{2} )$ |
| $1 - 53 x + 1100 x^{2} - 10547 x^{3} + 39601 x^{4}$ | |
| Frobenius angles: | $\pm0.0936959350875$, $\pm0.126927281034$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $30102$ | $1544292804$ | $62059590469656$ | $2459329592340224160$ | $97393786012966189230402$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $147$ | $38993$ | $7874982$ | $1568210761$ | $312079949157$ | $62103855200186$ | $12358664592573243$ | $2459374196900727601$ | $489415464197954253738$ | $97393677360720832652153$ |
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 $\F_{199}$.
Endomorphism algebra over $\F_{199}$| The isogeny class factors as 1.199.abb $\times$ 1.199.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 |
|---|---|---|
| 2.199.ab_als | $2$ | (not in LMFDB) |
| 2.199.b_als | $2$ | (not in LMFDB) |
| 2.199.cb_bqi | $2$ | (not in LMFDB) |