Invariants
Base field: | $\F_{73}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 15 x + 73 x^{2} )^{2}$ |
$1 - 30 x + 371 x^{2} - 2190 x^{3} + 5329 x^{4}$ | |
Frobenius angles: | $\pm0.159004799845$, $\pm0.159004799845$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $3$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3481$ | $27573001$ | $151264989184$ | $806711038270281$ | $4297927782030847561$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $44$ | $5172$ | $388838$ | $28407076$ | $2073217244$ | $151335766158$ | $11047410984668$ | $806460166467268$ | $58871586916879094$ | $4297625827388882772$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 3 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=47x^6+61x^5+69x^4+28x^3+54x^2+3x+40$
- $y^2=39x^6+68x^5+64x^4+27x^3+51x^2+51x+2$
- $y^2=18x^6+67x^5+34x^4+20x^3+24x^2+60x+59$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{73}$.
Endomorphism algebra over $\F_{73}$The isogeny class factors as 1.73.ap 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-67}) \)$)$ |
Base change
This is a primitive isogeny class.