Invariants
Base field: | $\F_{113}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 21 x + 113 x^{2} )^{2}$ |
$1 - 42 x + 667 x^{2} - 4746 x^{3} + 12769 x^{4}$ | |
Frobenius angles: | $\pm0.0498602789898$, $\pm0.0498602789898$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $1$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $8649$ | $157628025$ | $2075777851536$ | $26577696761555625$ | $339449650075636504569$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $72$ | $12340$ | $1438614$ | $163005988$ | $18423967032$ | $2081948347870$ | $235260520023384$ | $26584441725349828$ | $3004041936872685942$ | $339456738991898823700$ |
Jacobians and polarizations
This isogeny class contains the Jacobian of 1 curve (which is hyperelliptic), and hence is principally polarizable:
- $y^2=75x^6+7x^5+107x^4+109x^3+37x^2+81x+48$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{113}$.
Endomorphism algebra over $\F_{113}$The isogeny class factors as 1.113.av 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-11}) \)$)$ |
Base change
This is a primitive isogeny class.