Invariants
| Base field: | $\F_{193}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 47 x + 923 x^{2} - 9071 x^{3} + 37249 x^{4}$ |
| Frobenius angles: | $\pm0.0526881694498$, $\pm0.250841491310$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.30262893.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $26$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $29055$ | $1374040005$ | $51676117079535$ | $1925144786215617525$ | $71708910713168138108400$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $147$ | $36887$ | $7188165$ | $1387503739$ | $267785206002$ | $51682532469959$ | $9974730102163281$ | $1925122949467230931$ | $371548729883636735175$ | $71708904873338269761182$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 26 curves (of which all are hyperelliptic):
- $y^2=12 x^6+86 x^5+27 x^4+72 x^3+36 x^2+124 x+42$
- $y^2=167 x^6+85 x^5+51 x^4+8 x^3+122 x^2+15 x+183$
- $y^2=82 x^6+106 x^5+112 x^4+115 x^3+89 x^2+64 x+21$
- $y^2=155 x^6+85 x^5+9 x^4+133 x^3+105 x^2+103 x+119$
- $y^2=39 x^6+18 x^5+38 x^4+132 x^3+150 x^2+131 x+160$
- $y^2=181 x^6+43 x^5+176 x^4+50 x^3+165 x^2+126 x+17$
- $y^2=104 x^6+116 x^5+190 x^4+14 x^3+34 x^2+125 x+160$
- $y^2=80 x^6+54 x^5+23 x^4+155 x^3+184 x^2+13 x+119$
- $y^2=66 x^6+59 x^5+158 x^4+123 x^3+112 x^2+8 x+57$
- $y^2=20 x^6+162 x^5+24 x^4+168 x^3+4 x^2+152 x+130$
- $y^2=170 x^6+53 x^5+167 x^4+125 x^3+168 x^2+151 x+103$
- $y^2=163 x^6+143 x^5+11 x^4+149 x^3+10 x^2+10 x+41$
- $y^2=88 x^6+79 x^5+30 x^4+20 x^3+86 x^2+117 x+22$
- $y^2=76 x^6+145 x^5+96 x^4+8 x^3+185 x^2+74 x+123$
- $y^2=81 x^6+47 x^5+185 x^4+73 x^3+36 x^2+35 x+21$
- $y^2=100 x^6+184 x^5+97 x^4+177 x^3+155 x^2+28 x+192$
- $y^2=102 x^6+142 x^5+2 x^4+36 x^3+20 x^2+58 x+29$
- $y^2=92 x^6+125 x^5+119 x^4+177 x^3+146 x^2+150 x+36$
- $y^2=58 x^6+76 x^5+119 x^4+50 x^3+52 x^2+100 x+117$
- $y^2=19 x^6+132 x^5+133 x^4+127 x^3+123 x^2+80 x+180$
- $y^2=89 x^6+140 x^5+99 x^4+124 x^3+172 x^2+115 x+160$
- $y^2=136 x^6+39 x^5+161 x^4+89 x^3+65 x^2+129 x+37$
- $y^2=14 x^6+154 x^5+6 x^4+188 x^3+87 x^2+70 x+150$
- $y^2=149 x^6+15 x^5+92 x^4+88 x^3+117 x^2+125 x+102$
- $y^2=92 x^6+160 x^5+151 x^4+149 x^3+121 x^2+40 x+33$
- $y^2=111 x^6+90 x^5+98 x^4+14 x^3+118 x^2+12 x+86$
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 4.0.30262893.1. |
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.bv_bjn | $2$ | (not in LMFDB) |