Invariants
Base field: | $\F_{137}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 23 x + 137 x^{2} )^{2}$ |
$1 - 46 x + 803 x^{2} - 6302 x^{3} + 18769 x^{4}$ | |
Frobenius angles: | $\pm0.0596181899068$, $\pm0.0596181899068$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $13225$ | $342805225$ | $6597911449600$ | $124078565442015625$ | $2329168914662515605625$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $92$ | $18260$ | $2565926$ | $352220388$ | $48261203692$ | $6611851804430$ | $905824275416236$ | $124097929865711428$ | $17001416407462575542$ | $2329194047620840229300$ |
Jacobians and polarizations
This isogeny class contains the Jacobian of 1 curve (which is hyperelliptic), and hence is principally polarizable:
- $y^2=63x^6+124x^5+73x^4+89x^3+11x^2+83x+39$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{137}$.
Endomorphism algebra over $\F_{137}$The isogeny class factors as 1.137.ax 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-19}) \)$)$ |
Base change
This is a primitive isogeny class.