Invariants
| Base field: | $\F_{73}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 26 x + 312 x^{2} - 1898 x^{3} + 5329 x^{4}$ |
| Frobenius angles: | $\pm0.169131288727$, $\pm0.270807491780$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.1781568.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $24$ |
| Isomorphism classes: | 24 |
This isogeny class is simple and geometrically 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $3718$ | $28130388$ | $151749727558$ | $806911965706704$ | $4297876417553042038$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $48$ | $5278$ | $390084$ | $28414150$ | $2073192468$ | $151334706094$ | $11047397793984$ | $806460067987390$ | $58871586579459936$ | $4297625829880296238$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):
- $y^2=20 x^6+4 x^5+47 x^4+41 x^3+37 x^2+38 x+15$
- $y^2=56 x^6+46 x^5+14 x^4+10 x^3+21 x^2+56 x+23$
- $y^2=37 x^6+59 x^5+55 x^4+10 x^3+58 x^2+25 x+27$
- $y^2=30 x^6+56 x^5+29 x^4+52 x^3+3 x^2+48 x+1$
- $y^2=70 x^6+57 x^5+49 x^4+41 x^3+38 x^2+21 x+20$
- $y^2=15 x^6+2 x^5+x^4+65 x^3+12 x^2+69 x+66$
- $y^2=20 x^6+35 x^5+51 x^4+51 x^3+59 x^2+68 x+11$
- $y^2=9 x^6+52 x^5+33 x^4+45 x^3+12 x^2+28 x+29$
- $y^2=22 x^6+72 x^5+29 x^4+21 x^3+69 x^2+72 x+59$
- $y^2=32 x^6+17 x^5+63 x^4+44 x^3+10 x^2+53 x+52$
- $y^2=40 x^6+72 x^5+25 x^4+22 x^3+70 x^2+58 x+55$
- $y^2=63 x^6+66 x^5+28 x^4+55 x^3+7 x^2+10 x+11$
- $y^2=46 x^6+31 x^5+13 x^4+66 x^3+15 x^2+52 x+17$
- $y^2=37 x^6+25 x^5+43 x^4+2 x^3+35 x^2+43 x+44$
- $y^2=42 x^6+32 x^5+72 x^4+39 x^3+56 x^2+66 x+53$
- $y^2=67 x^6+4 x^5+9 x^4+35 x^3+62 x^2+22 x+42$
- $y^2=46 x^6+23 x^5+18 x^4+23 x^3+45 x^2+52 x+51$
- $y^2=48 x^6+10 x^5+42 x^4+9 x^3+42 x^2+15 x+68$
- $y^2=7 x^6+36 x^5+68 x^4+9 x^3+48 x^2+23 x+58$
- $y^2=33 x^6+56 x^5+46 x^4+42 x^3+29 x^2+48 x+43$
- $y^2=69 x^6+4 x^5+20 x^4+10 x^3+34 x^2+x+15$
- $y^2=35 x^6+36 x^5+69 x^4+56 x^3+9 x^2+31 x+39$
- $y^2=54 x^6+6 x^5+53 x^4+72 x^3+21 x^2+40 x+10$
- $y^2=44 x^6+37 x^5+41 x^4+14 x^3+32 x^2+3 x+17$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{73}$.
Endomorphism algebra over $\F_{73}$| The endomorphism algebra of this simple isogeny class is 4.0.1781568.1. |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
| Twist | Extension degree | Common base change |
|---|---|---|
| 2.73.ba_ma | $2$ | (not in LMFDB) |