Invariants
Base field: | $\F_{199}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 28 x + 199 x^{2} )( 1 - 27 x + 199 x^{2} )$ |
$1 - 55 x + 1154 x^{2} - 10945 x^{3} + 39601 x^{4}$ | |
Frobenius angles: | $\pm0.0391815390403$, $\pm0.0936959350875$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $29756$ | $1540051536$ | $62034525741104$ | $2459217132947674944$ | $97393358188810034661476$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $145$ | $38885$ | $7871800$ | $1568139049$ | $312078578275$ | $62103832003406$ | $12358664238953485$ | $2459374192033203889$ | $489415464138299521000$ | $97393677360098926549325$ |
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.abc $\times$ 1.199.abb 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.