Invariants
| Base field: | $\F_{191}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 49 x + 975 x^{2} - 9359 x^{3} + 36481 x^{4}$ |
| Frobenius angles: | $\pm0.0573856553654$, $\pm0.210617421473$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.5958485.4 |
| Galois group: | $D_{4}$ |
| Jacobians: | $20$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $28049$ | $1314516385$ | $48534500731031$ | $1771209806888796365$ | $64615141893324404297104$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $143$ | $36031$ | $6965471$ | $1330872771$ | $254195270628$ | $48551229145963$ | $9273284175057773$ | $1771197283850101011$ | $338298681526652651681$ | $64615048177515038883726$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 20 curves (of which all are hyperelliptic):
- $y^2=86 x^6+108 x^5+76 x^4+132 x^3+150 x^2+5 x+28$
- $y^2=142 x^6+140 x^5+22 x^4+110 x^3+89 x^2+176$
- $y^2=79 x^6+189 x^5+118 x^4+42 x^3+151 x^2+49 x+37$
- $y^2=139 x^6+14 x^5+141 x^4+170 x^3+167 x^2+62 x+31$
- $y^2=176 x^6+136 x^5+13 x^4+157 x^3+44 x^2+129 x+45$
- $y^2=131 x^6+3 x^5+41 x^4+41 x^3+x^2+175 x+172$
- $y^2=102 x^6+166 x^5+37 x^4+144 x^3+87 x^2+68 x+160$
- $y^2=179 x^6+101 x^5+74 x^4+34 x^3+109 x^2+114 x+187$
- $y^2=26 x^6+x^5+96 x^4+188 x^3+86 x^2+123 x+121$
- $y^2=78 x^6+142 x^5+155 x^4+171 x^3+21 x^2+55 x+47$
- $y^2=145 x^6+156 x^5+117 x^4+142 x^3+122 x^2+150 x+161$
- $y^2=76 x^6+8 x^5+177 x^4+94 x^3+41 x^2+52 x+71$
- $y^2=146 x^6+174 x^5+129 x^4+57 x^3+118 x^2+84 x+22$
- $y^2=127 x^6+84 x^5+64 x^4+47 x^3+143 x^2+93 x+7$
- $y^2=30 x^6+89 x^5+161 x^4+66 x^3+126 x^2+187 x+89$
- $y^2=29 x^6+156 x^5+49 x^4+146 x^3+116 x^2+80 x+14$
- $y^2=85 x^6+165 x^5+47 x^4+184 x^3+57 x^2+58 x+177$
- $y^2=75 x^6+19 x^5+113 x^4+30 x^3+82 x^2+126 x+153$
- $y^2=123 x^6+65 x^5+33 x^4+57 x^3+180 x^2+125 x+41$
- $y^2=127 x^6+126 x^5+125 x^4+33 x^3+96 x^2+42 x+34$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{191}$.
Endomorphism algebra over $\F_{191}$| The endomorphism algebra of this simple isogeny class is 4.0.5958485.4. |
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 |
|---|---|---|
| 2.191.bx_bln | $2$ | (not in LMFDB) |