Invariants
| Base field: | $\F_{179}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 47 x + 906 x^{2} - 8413 x^{3} + 32041 x^{4}$ |
| Frobenius angles: | $\pm0.0955537064913$, $\pm0.204199342431$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.1159757.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $22$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $24488$ | $1013999104$ | $32886572271776$ | $1053991686989355008$ | $33770087832404015844088$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $133$ | $31645$ | $5734024$ | $1026656265$ | $183766792563$ | $32894124781654$ | $5888046418057321$ | $1053960289568211153$ | $188658891711954915064$ | $33769941616282891573005$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 22 curves (of which all are hyperelliptic):
- $y^2=14 x^6+135 x^5+39 x^4+90 x^3+156 x^2+52 x+37$
- $y^2=36 x^6+x^5+11 x^4+x^3+156 x^2+115 x+119$
- $y^2=72 x^6+37 x^5+134 x^4+21 x^3+28 x^2+42 x+48$
- $y^2=20 x^6+46 x^5+31 x^4+14 x^3+94 x^2+158 x+113$
- $y^2=44 x^6+175 x^5+69 x^4+12 x^3+131 x^2+75 x+134$
- $y^2=151 x^6+66 x^5+21 x^4+87 x^3+112 x^2+18 x$
- $y^2=135 x^6+122 x^5+6 x^4+141 x^3+111 x^2+69 x+79$
- $y^2=134 x^6+130 x^5+148 x^4+20 x^3+81 x^2+84 x+155$
- $y^2=98 x^6+135 x^5+117 x^4+35 x^3+168 x^2+54 x+132$
- $y^2=110 x^6+75 x^5+175 x^4+111 x^3+110 x^2+176 x+19$
- $y^2=138 x^6+43 x^5+49 x^4+97 x^3+30 x^2+28 x+104$
- $y^2=134 x^6+127 x^5+42 x^4+29 x^3+20 x^2+52 x+98$
- $y^2=66 x^6+176 x^5+136 x^4+76 x^3+11 x^2+30 x+86$
- $y^2=128 x^6+161 x^5+176 x^4+176 x^3+83 x^2+80 x+26$
- $y^2=8 x^6+162 x^5+84 x^4+3 x^3+27 x^2+106 x+115$
- $y^2=124 x^6+23 x^5+91 x^4+30 x^3+55 x^2+49 x+9$
- $y^2=84 x^6+153 x^5+58 x^4+66 x^3+51 x^2+152 x+115$
- $y^2=111 x^6+104 x^5+24 x^4+130 x^3+167 x^2+69 x+157$
- $y^2=104 x^6+116 x^5+132 x^4+87 x^3+89 x^2+114 x+35$
- $y^2=81 x^6+20 x^5+56 x^4+47 x^3+93 x^2+163 x+139$
- $y^2=141 x^6+167 x^5+162 x^4+67 x^3+62 x^2+168 x+71$
- $y^2=94 x^6+134 x^5+6 x^4+43 x^3+156 x^2+92 x+176$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{179}$.
Endomorphism algebra over $\F_{179}$| The endomorphism algebra of this simple isogeny class is 4.0.1159757.1. |
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 |
|---|---|---|
| 2.179.bv_biw | $2$ | (not in LMFDB) |