Invariants
| Base field: | $\F_{191}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 47 x + 918 x^{2} - 8977 x^{3} + 36481 x^{4}$ |
| Frobenius angles: | $\pm0.0283325455262$, $\pm0.251234528562$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.2454725.2 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $28376$ | $1317327424$ | $48542051259296$ | $1771203361377922304$ | $64614994523053342297576$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $145$ | $36109$ | $6966556$ | $1330867929$ | $254194690875$ | $48551213953198$ | $9273283921836205$ | $1771197280976822289$ | $338298681508885141396$ | $64615048177578266133429$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 20 curves (of which all are hyperelliptic):
- $y^2=50 x^6+34 x^5+99 x^4+139 x^3+136 x^2+151 x+127$
- $y^2=88 x^6+161 x^5+92 x^4+143 x^3+80 x^2+113 x+110$
- $y^2=122 x^6+x^5+34 x^4+78 x^3+144 x^2+176 x+38$
- $y^2=45 x^6+187 x^5+78 x^4+183 x^3+32 x^2+140 x+28$
- $y^2=11 x^6+182 x^5+49 x^4+139 x^3+41 x^2+180 x+25$
- $y^2=24 x^6+76 x^5+190 x^4+45 x^3+102 x^2+107 x+63$
- $y^2=94 x^6+38 x^5+7 x^4+106 x^3+26 x^2+90 x+32$
- $y^2=46 x^6+11 x^5+96 x^4+11 x^3+25 x^2+118 x+151$
- $y^2=129 x^6+171 x^5+39 x^3+142 x^2+185 x+166$
- $y^2=80 x^6+136 x^5+66 x^4+184 x^3+30 x^2+77 x+157$
- $y^2=92 x^6+122 x^5+127 x^4+50 x^3+189 x^2+15 x+84$
- $y^2=81 x^6+14 x^5+110 x^4+46 x^3+15 x^2+33 x+139$
- $y^2=152 x^6+132 x^5+33 x^4+100 x^3+62 x^2+44 x+37$
- $y^2=68 x^6+182 x^5+110 x^4+128 x^3+14 x^2+110 x+101$
- $y^2=31 x^6+78 x^5+150 x^4+117 x^3+35 x^2+77 x+118$
- $y^2=159 x^6+50 x^5+154 x^4+15 x^3+68 x^2+22 x+22$
- $y^2=129 x^6+40 x^5+117 x^4+94 x^3+149 x^2+161 x+142$
- $y^2=35 x^6+104 x^5+122 x^4+2 x^3+136 x^2+139 x+108$
- $y^2=139 x^6+21 x^5+144 x^4+189 x^3+183 x^2+80 x+186$
- $y^2=168 x^6+49 x^5+40 x^4+59 x^3+97 x^2+19 x+161$
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 4.0.2454725.2. |
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.bv_bji | $2$ | (not in LMFDB) |