Invariants
Base field: | $\F_{79}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 15 x + 79 x^{2} )( 1 - 13 x + 79 x^{2} )$ |
$1 - 28 x + 353 x^{2} - 2212 x^{3} + 6241 x^{4}$ | |
Frobenius angles: | $\pm0.180303926787$, $\pm0.238910621905$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $14$ |
Isomorphism classes: | 20 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4355$ | $38476425$ | $243613195280$ | $1517901776577225$ | $9468880838430678275$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $52$ | $6164$ | $494104$ | $38970436$ | $3077252932$ | $243088613822$ | $19203910425388$ | $1517108749024516$ | $119851595105476936$ | $9468276075512872724$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=77x^6+60x^5+16x^4+26x^3+26x^2+35x+59$
- $y^2=43x^6+2x^5+75x^4+13x^3+43x^2+4x+63$
- $y^2=38x^6+57x^5+32x^3+77x+8$
- $y^2=41x^6+19x^5+26x^4+63x^3+18x^2+25x+14$
- $y^2=75x^6+30x^5+42x^4+73x^3+52x^2+39x+53$
- $y^2=47x^6+31x^5+9x^4+75x^3+72x^2+9x+48$
- $y^2=63x^6+24x^5+62x^4+11x^3+67x^2+30x+37$
- $y^2=53x^6+72x^5+30x^4+75x^3+27x^2+52x+70$
- $y^2=47x^6+62x^5+51x^4+55x^3+38x^2+36x+74$
- $y^2=23x^6+9x^5+53x^4+60x^3+35x^2+x+5$
- $y^2=72x^6+47x^5+35x^4+53x^3+69x^2+78x+5$
- $y^2=66x^6+72x^5+12x^4+23x^3+35x^2+20x+3$
- $y^2=55x^6+27x^5+55x^4+47x^3+76x^2+14x+16$
- $y^2=29x^6+45x^5+66x^4+38x^3+58x^2+23x+60$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{79}$.
Endomorphism algebra over $\F_{79}$The isogeny class factors as 1.79.ap $\times$ 1.79.an 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.