Invariants
| Base field: | $\F_{79}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 14 x + 79 x^{2} )^{2}$ |
| $1 - 28 x + 354 x^{2} - 2212 x^{3} + 6241 x^{4}$ | |
| Frobenius angles: | $\pm0.211343260462$, $\pm0.211343260462$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $24$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4356$ | $38489616$ | $243654780996$ | $1517968871654400$ | $9468948043662723396$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $52$ | $6166$ | $494188$ | $38972158$ | $3077274772$ | $243088768726$ | $19203910119628$ | $1517108722031998$ | $119851594662830452$ | $9468276071091907606$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):
- $y^2=43 x^6+30 x^4+30 x^2+43$
- $y^2=2 x^5+18 x^4+76 x^3+60 x^2+6 x+6$
- $y^2=73 x^6+70 x^5+47 x^4+64 x^3+77 x^2+8 x+68$
- $y^2=39 x^6+50 x^5+32 x^4+32 x^3+42 x^2+67 x+60$
- $y^2=11 x^6+28 x^5+x^4+26 x^3+32 x^2+74 x+50$
- $y^2=69 x^6+73 x^5+42 x^4+53 x^3+37 x^2+18 x+74$
- $y^2=27 x^6+78 x^5+62 x^4+27 x^3+23 x^2+29 x+70$
- $y^2=20 x^6+72 x^5+72 x^4+50 x^3+27 x^2+39 x+77$
- $y^2=30 x^6+48 x^5+25 x^4+9 x^3+75 x^2+3 x+56$
- $y^2=x^6+x^3+8$
- $y^2=60 x^6+16 x^5+72 x^4+7 x^3+32 x^2+49 x+29$
- $y^2=66 x^6+65 x^5+45 x^4+56 x^3+78 x^2+29 x+75$
- $y^2=14 x^6+48 x^5+8 x^4+73 x^3+18 x^2+37 x+12$
- $y^2=50 x^6+8 x^5+30 x^4+74 x^3+30 x^2+8 x+50$
- $y^2=74 x^6+12 x^5+73 x^4+61 x^3+73 x^2+12 x+74$
- $y^2=11 x^6+37 x^5+26 x^4+63 x^3+59 x^2+37 x+68$
- $y^2=41 x^6+11 x^5+58 x^4+67 x^3+58 x^2+11 x+41$
- $y^2=55 x^6+11 x^5+26 x^4+68 x^3+26 x^2+11 x+55$
- $y^2=73 x^6+54 x^4+54 x^2+73$
- $y^2=27 x^6+55 x^5+69 x^4+57 x^3+69 x^2+55 x+27$
- $y^2=49 x^6+4 x^5+14 x^4+47 x^3+20 x^2+39 x+31$
- $y^2=x^6+73 x^5+70 x^4+57 x^3+70 x^2+73 x+1$
- $y^2=x^6+72 x^3+52$
- $y^2=34 x^6+32 x^5+67 x^4+76 x^3+32 x^2+52 x+37$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{79}$.
Endomorphism algebra over $\F_{79}$| The isogeny class factors as 1.79.ao 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-30}) \)$)$ |
Base change
This is a primitive isogeny class.