Invariants
| Base field: | $\F_{73}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 + 14 x + 73 x^{2} )^{2}$ |
| $1 + 28 x + 342 x^{2} + 2044 x^{3} + 5329 x^{4}$ | |
| Frobenius angles: | $\pm0.805631034678$, $\pm0.805631034678$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $29$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $7744$ | $27878400$ | $151084580416$ | $806923560960000$ | $4297249762013268544$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $102$ | $5230$ | $388374$ | $28414558$ | $2072890182$ | $151335574990$ | $11047392880374$ | $806460072381118$ | $58871587393076262$ | $4297625821540687150$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 29 curves (of which all are hyperelliptic):
- $y^2=23 x^6+52 x^5+49 x^4+17 x^3+x^2+30 x+37$
- $y^2=31 x^6+16 x^5+37 x^4+64 x^3+49 x^2+72 x+20$
- $y^2=64 x^6+53 x^4+53 x^2+64$
- $y^2=25 x^6+44 x^5+42 x^4+63 x^3+51 x^2+35 x+36$
- $y^2=19 x^6+22 x^5+70 x^4+24 x^3+35 x^2+42 x+48$
- $y^2=24 x^6+66 x^4+66 x^2+24$
- $y^2=2 x^6+46 x^5+37 x^4+36 x^3+48 x^2+25 x+25$
- $y^2=69 x^6+60 x^4+60 x^2+69$
- $y^2=55 x^6+3 x^5+42 x^4+48 x^3+43 x^2+6 x+57$
- $y^2=35 x^6+14 x^5+53 x^4+53 x^3+64 x^2+59 x+14$
- $y^2=3 x^6+3 x^5+23 x^4+48 x^3+9 x^2+37 x+65$
- $y^2=49 x^6+58 x^5+9 x^4+66 x^3+71 x^2+29 x+27$
- $y^2=61 x^6+27 x^4+27 x^2+61$
- $y^2=5 x^6+5 x^3+62$
- $y^2=31 x^6+31 x^4+31 x^2+31$
- $y^2=15 x^6+47 x^5+32 x^4+7 x^3+32 x^2+47 x+15$
- $y^2=67 x^6+61 x^5+69 x^4+34 x^3+65 x^2+25 x+25$
- $y^2=67 x^6+54 x^5+9 x^4+51 x^3+3 x^2+6 x+16$
- $y^2=9 x^6+35 x^5+47 x^4+4 x^3+47 x^2+35 x+9$
- $y^2=2 x^6+54 x^5+27 x^4+34 x^3+27 x^2+54 x+2$
- $y^2=5 x^6+52 x^3+15$
- $y^2=45 x^6+38 x^5+35 x^4+40 x^3+71 x^2+59 x+50$
- $y^2=2 x^6+57 x^5+5 x^4+40 x^3+5 x^2+57 x+2$
- $y^2=57 x^6+64 x^5+56 x^4+71 x^3+15 x^2+18 x+19$
- $y^2=5 x^6+39 x^3+28$
- $y^2=4 x^6+12 x^5+30 x^4+38 x^3+11 x^2+24 x+37$
- $y^2=21 x^6+38 x^5+10 x^4+7 x^3+10 x^2+38 x+21$
- $y^2=46 x^6+43 x^5+53 x^4+70 x^3+17 x^2+13 x+24$
- $y^2=71 x^6+21 x^5+26 x^4+67 x^3+26 x^2+21 x+71$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{73}$.
Endomorphism algebra over $\F_{73}$| The isogeny class factors as 1.73.o 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-6}) \)$)$ |
Base change
This is a primitive isogeny class.