Invariants
| Base field: | $\F_{193}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 48 x + 955 x^{2} - 9264 x^{3} + 37249 x^{4}$ |
| Frobenius angles: | $\pm0.0914626496846$, $\pm0.220975467824$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.15360912.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $24$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $28893$ | $1372908681$ | $51676334413524$ | $1925177234878552761$ | $71709130057453807360773$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $146$ | $36856$ | $7188194$ | $1387527124$ | $267786025106$ | $51682550223526$ | $9974730381908690$ | $1925122952696370148$ | $371548729907588680418$ | $71708904873371922778696$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):
- $y^2=40 x^6+115 x^5+24 x^4+141 x^3+186 x^2+12 x+70$
- $y^2=106 x^6+77 x^5+38 x^4+22 x^3+127 x^2+141 x+132$
- $y^2=2 x^6+118 x^5+32 x^4+3 x^3+19 x^2+96 x+149$
- $y^2=102 x^6+17 x^5+129 x^4+165 x^3+85 x^2+190 x+140$
- $y^2=91 x^6+154 x^5+6 x^4+15 x^3+165 x^2+59 x+54$
- $y^2=102 x^6+144 x^5+157 x^4+16 x^3+171 x^2+44 x+7$
- $y^2=150 x^6+43 x^5+86 x^4+54 x^3+31 x^2+63 x+30$
- $y^2=152 x^6+65 x^5+35 x^4+113 x^3+91 x^2+130 x+135$
- $y^2=111 x^6+84 x^5+25 x^4+175 x^3+134 x^2+162 x+146$
- $y^2=10 x^6+110 x^5+136 x^4+46 x^3+156 x^2+125 x+66$
- $y^2=88 x^6+70 x^5+165 x^4+15 x^3+136 x^2+109 x+150$
- $y^2=138 x^6+51 x^5+181 x^4+101 x^3+141 x^2+111 x+13$
- $y^2=111 x^6+83 x^5+6 x^4+169 x^3+156 x^2+73 x+130$
- $y^2=10 x^6+14 x^5+127 x^4+113 x^3+141 x^2+143 x+37$
- $y^2=69 x^6+22 x^5+151 x^4+133 x^3+104 x^2+65 x+16$
- $y^2=17 x^6+130 x^5+189 x^4+186 x^3+126 x^2+107 x+65$
- $y^2=187 x^6+47 x^5+12 x^4+89 x^3+52 x^2+188 x+141$
- $y^2=93 x^6+144 x^5+185 x^4+149 x^3+147 x^2+10 x+119$
- $y^2=45 x^6+56 x^5+143 x^4+30 x^3+107 x^2+68 x+10$
- $y^2=66 x^6+178 x^5+41 x^4+106 x^3+146 x^2+47 x+134$
- $y^2=51 x^6+14 x^5+101 x^4+64 x^3+181 x^2+122 x+157$
- $y^2=44 x^6+132 x^5+x^4+39 x^3+138 x^2+105 x+18$
- $y^2=61 x^6+123 x^5+65 x^4+62 x^3+65 x^2+80 x+153$
- $y^2=81 x^6+45 x^5+151 x^4+170 x^3+24 x^2+97 x+44$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{193}$.
Endomorphism algebra over $\F_{193}$| The endomorphism algebra of this simple isogeny class is 4.0.15360912.1. |
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 |
|---|---|---|
| 2.193.bw_bkt | $2$ | (not in LMFDB) |