Invariants
| Base field: | $\F_{163}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 44 x + 798 x^{2} - 7172 x^{3} + 26569 x^{4}$ |
| Frobenius angles: | $\pm0.0236068181920$, $\pm0.241413415058$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.39744.5 |
| Galois group: | $D_{4}$ |
| Jacobians: | $28$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $20152$ | $696936768$ | $18749460156856$ | $498312833339802624$ | $13239625329965910743032$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $120$ | $26230$ | $4329384$ | $705913774$ | $115063524600$ | $18755363155750$ | $3057125083076520$ | $498311411768505694$ | $81224760504261240312$ | $13239635966787143560150$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 28 curves (of which all are hyperelliptic):
- $y^2=89 x^6+117 x^5+116 x^4+110 x^3+60 x^2+151 x+131$
- $y^2=12 x^6+5 x^5+105 x^4+44 x^3+39 x^2+8 x+106$
- $y^2=2 x^6+101 x^5+145 x^4+135 x^3+52 x^2+39 x+26$
- $y^2=98 x^6+18 x^5+113 x^4+82 x^3+78 x+98$
- $y^2=59 x^6+56 x^5+93 x^4+162 x^3+14 x^2+x+52$
- $y^2=11 x^6+90 x^5+26 x^4+57 x^3+117 x^2+72 x+65$
- $y^2=130 x^6+5 x^5+51 x^4+151 x^3+120 x^2+116 x+127$
- $y^2=105 x^6+136 x^5+17 x^4+10 x^3+36 x^2+32 x+130$
- $y^2=38 x^6+43 x^5+46 x^4+156 x^3+15 x^2+55 x+136$
- $y^2=117 x^6+136 x^5+10 x^4+59 x^3+78 x^2+130 x+116$
- $y^2=21 x^6+31 x^5+110 x^4+155 x^3+26 x^2+133 x+81$
- $y^2=73 x^6+112 x^5+4 x^4+56 x^3+123 x^2+62 x+106$
- $y^2=70 x^6+116 x^5+141 x^4+39 x^3+51 x^2+143 x+68$
- $y^2=29 x^6+127 x^5+62 x^4+45 x^3+132 x^2+117 x+146$
- $y^2=116 x^6+54 x^5+47 x^4+150 x^3+106 x^2+155 x+5$
- $y^2=159 x^6+113 x^5+22 x^4+105 x^3+25 x^2+52 x+79$
- $y^2=129 x^6+138 x^5+84 x^4+157 x^3+41 x^2+108 x+130$
- $y^2=122 x^6+140 x^5+82 x^4+32 x^3+41 x^2+45 x+107$
- $y^2=96 x^6+6 x^5+19 x^4+103 x^3+117 x^2+112 x+81$
- $y^2=88 x^6+54 x^5+85 x^4+88 x^3+79 x^2+20 x+60$
- $y^2=14 x^6+129 x^5+29 x^4+97 x^3+70 x^2+140 x+82$
- $y^2=141 x^6+96 x^5+56 x^4+33 x^3+66 x^2+106 x+8$
- $y^2=29 x^6+155 x^5+67 x^4+155 x^3+70 x^2+156 x+31$
- $y^2=24 x^6+58 x^5+138 x^4+96 x^3+113 x^2+70 x+25$
- $y^2=34 x^6+85 x^5+92 x^4+108 x^3+138 x^2+137 x+15$
- $y^2=32 x^6+98 x^5+88 x^4+154 x^3+155 x^2+127 x+127$
- $y^2=113 x^6+26 x^5+52 x^4+79 x^3+102 x^2+64 x+147$
- $y^2=78 x^6+124 x^5+151 x^4+70 x^3+48 x^2+121 x+68$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{163}$.
Endomorphism algebra over $\F_{163}$| The endomorphism algebra of this simple isogeny class is 4.0.39744.5. |
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 |
|---|---|---|
| 2.163.bs_bes | $2$ | (not in LMFDB) |