Invariants
Base field: | $\F_{73}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 16 x + 73 x^{2} )^{2}$ |
$1 - 32 x + 402 x^{2} - 2336 x^{3} + 5329 x^{4}$ | |
Frobenius angles: | $\pm0.114200251220$, $\pm0.114200251220$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $5$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3364$ | $27248400$ | $150874757476$ | $806378250240000$ | $4297709354163860644$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $42$ | $5110$ | $387834$ | $28395358$ | $2073111882$ | $151335081430$ | $11047409260314$ | $806460201328318$ | $58871587675106922$ | $4297625837184282550$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 5 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=5x^6+5x^3+47$
- $y^2=62x^6+63x^4+63x^2+62$
- $y^2=40x^6+12x^5+39x^4+70x^3+21x^2+70x+62$
- $y^2=5x^6+5x^3+33$
- $y^2=35x^6+48x^5+10x^4+21x^3+31x^2+70x+32$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{73}$.
Endomorphism algebra over $\F_{73}$The isogeny class factors as 1.73.aq 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-1}) \)$)$ |
Base change
This is a primitive isogeny class.