Invariants
| Base field: | $\F_{179}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 46 x + 884 x^{2} - 8234 x^{3} + 32041 x^{4}$ |
| Frobenius angles: | $\pm0.124666363590$, $\pm0.207564932480$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.3961152.8 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $24646$ | $1015563076$ | $32893857764062$ | $1054016669103091408$ | $33770157588649505674366$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $134$ | $31694$ | $5735294$ | $1026680598$ | $183767172154$ | $32894129732366$ | $5888046470590978$ | $1053960289949796574$ | $188658891711412168742$ | $33769941616188670342814$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):
- $y^2=144 x^6+103 x^5+121 x^4+153 x^3+116 x^2+117 x+173$
- $y^2=35 x^6+84 x^5+72 x^4+33 x^3+97 x^2+85 x+109$
- $y^2=x^6+153 x^5+87 x^4+131 x^3+60 x^2+167 x$
- $y^2=133 x^6+74 x^5+164 x^4+169 x^3+104 x^2+174 x+41$
- $y^2=88 x^6+88 x^5+54 x^4+55 x^3+30 x^2+20 x+171$
- $y^2=102 x^6+148 x^5+48 x^4+66 x^3+142 x^2+170 x+55$
- $y^2=62 x^6+42 x^5+85 x^4+3 x^3+86 x^2+130 x+161$
- $y^2=78 x^5+44 x^4+136 x^3+127 x^2+168 x+104$
- $y^2=4 x^6+61 x^5+56 x^4+78 x^3+56 x^2+159 x+176$
- $y^2=176 x^6+108 x^5+34 x^4+31 x^3+91 x^2+6 x+157$
- $y^2=107 x^6+16 x^5+90 x^4+176 x^3+73 x^2+147 x+4$
- $y^2=114 x^6+74 x^5+83 x^4+141 x^3+50 x^2+73 x+42$
- $y^2=165 x^6+44 x^5+160 x^4+67 x^3+95 x^2+13 x+174$
- $y^2=175 x^6+60 x^5+117 x^4+156 x^3+29 x^2+26 x+141$
- $y^2=131 x^6+125 x^5+129 x^4+82 x^3+38 x^2+137 x+112$
- $y^2=167 x^6+11 x^5+130 x^4+17 x^3+102 x^2+27 x+133$
- $y^2=161 x^6+57 x^5+6 x^4+35 x^3+85 x^2+80 x+42$
- $y^2=53 x^6+90 x^5+178 x^4+145 x^3+18 x^2+38 x+21$
- $y^2=24 x^6+25 x^5+122 x^4+154 x^3+129 x^2+95 x+98$
- $y^2=113 x^6+40 x^5+67 x^4+32 x^3+76 x^2+160 x+68$
- $y^2=139 x^6+46 x^5+123 x^4+65 x^3+86 x^2+12 x+73$
- $y^2=162 x^6+67 x^5+22 x^4+109 x^3+76 x^2+49 x+156$
- $y^2=96 x^6+29 x^5+97 x^4+30 x^3+105 x^2+41 x+118$
- $y^2=32 x^6+151 x^5+16 x^4+12 x^3+49 x^2+160 x+72$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{179}$.
Endomorphism algebra over $\F_{179}$| The endomorphism algebra of this simple isogeny class is 4.0.3961152.8. |
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 |
|---|---|---|
| 2.179.bu_bia | $2$ | (not in LMFDB) |