Invariants
| Base field: | $\F_{127}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 39 x + 631 x^{2} - 4953 x^{3} + 16129 x^{4}$ |
| Frobenius angles: | $\pm0.105907691525$, $\pm0.212566609663$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.198237.2 |
| Galois group: | $D_{4}$ |
| Jacobians: | $24$ |
| Isomorphism classes: | 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $11769$ | $256011057$ | $4195156167423$ | $67680720731251629$ | $1091546743269533167824$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $89$ | $15871$ | $2048033$ | $260165731$ | $33038759564$ | $4195877262523$ | $532875893657651$ | $67675234396028179$ | $8594754748763206439$ | $1091533853077341604366$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):
- $y^2=97 x^6+24 x^5+95 x^4+52 x^3+19 x^2+112 x+65$
- $y^2=75 x^6+5 x^5+109 x^4+68 x^3+55 x^2+120 x+5$
- $y^2=41 x^6+93 x^5+31 x^4+69 x^3+61 x^2+47 x+94$
- $y^2=93 x^6+62 x^5+124 x^4+11 x^3+66 x^2+5 x+12$
- $y^2=126 x^6+20 x^5+98 x^4+76 x^3+49 x^2+100 x+82$
- $y^2=106 x^6+59 x^5+123 x^4+39 x^3+32 x^2+28$
- $y^2=34 x^6+7 x^5+91 x^4+65 x^3+120 x^2+35 x+86$
- $y^2=57 x^6+95 x^5+81 x^4+55 x^3+116 x^2+70 x+33$
- $y^2=53 x^6+15 x^5+47 x^4+16 x^3+115 x^2+61 x+53$
- $y^2=38 x^6+118 x^5+42 x^4+46 x^3+58 x^2+119 x+40$
- $y^2=8 x^6+84 x^5+103 x^4+93 x^3+123 x^2+3 x+56$
- $y^2=43 x^6+112 x^5+6 x^4+27 x^3+8 x^2+116 x+54$
- $y^2=118 x^6+59 x^5+116 x^4+96 x^3+27 x^2+16 x+108$
- $y^2=35 x^6+79 x^5+64 x^4+66 x^3+88 x^2+33 x+54$
- $y^2=7 x^6+55 x^5+83 x^4+77 x^3+51 x^2+116 x+38$
- $y^2=78 x^6+34 x^5+7 x^3+59 x^2+103 x+28$
- $y^2=97 x^6+123 x^5+75 x^4+67 x^3+42 x^2+58 x+82$
- $y^2=26 x^6+10 x^5+89 x^4+117 x^3+88 x^2+34 x+119$
- $y^2=23 x^6+120 x^5+12 x^4+10 x^3+83 x^2+17 x+102$
- $y^2=75 x^6+92 x^5+23 x^4+117 x^3+85 x^2+2 x+96$
- $y^2=28 x^6+49 x^5+75 x^4+125 x^3+104 x^2+59 x+60$
- $y^2=3 x^6+98 x^5+114 x^4+104 x^3+112 x^2+50 x+100$
- $y^2=14 x^6+39 x^4+88 x^3+28 x^2+107 x+65$
- $y^2=90 x^6+77 x^5+29 x^4+35 x^3+109 x^2+69 x+11$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{127}$.
Endomorphism algebra over $\F_{127}$| The endomorphism algebra of this simple isogeny class is 4.0.198237.2. |
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 |
|---|---|---|
| 2.127.bn_yh | $2$ | (not in LMFDB) |