Invariants
| Base field: | $\F_{127}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 37 x + 582 x^{2} - 4699 x^{3} + 16129 x^{4}$ |
| Frobenius angles: | $\pm0.0487612671148$, $\pm0.273375674829$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.2797389.2 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $11976$ | $256861248$ | $4195567648800$ | $67676401215515904$ | $1091530074601593581496$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $91$ | $15925$ | $2048236$ | $260149129$ | $33038255041$ | $4195868682670$ | $532875793613863$ | $67675233631862449$ | $8594754746762028292$ | $1091533853115101990125$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):
- $y^2=63 x^6+124 x^5+116 x^4+27 x^3+79 x^2+69 x+111$
- $y^2=98 x^5+8 x^4+96 x^3+46 x^2+99 x+109$
- $y^2=55 x^6+32 x^5+124 x^4+112 x^3+40 x^2+123 x+36$
- $y^2=116 x^6+98 x^5+69 x^4+91 x^3+91 x^2+10 x+79$
- $y^2=40 x^6+15 x^5+108 x^4+118 x^3+125 x^2+70 x+6$
- $y^2=66 x^6+12 x^5+107 x^4+126 x^3+25 x^2+47 x+26$
- $y^2=94 x^6+8 x^5+70 x^4+112 x^3+20 x^2+22 x+40$
- $y^2=50 x^6+50 x^5+69 x^4+12 x^3+77 x^2+80 x+21$
- $y^2=11 x^6+65 x^5+114 x^4+110 x^3+84 x^2+116 x+102$
- $y^2=114 x^6+58 x^5+60 x^4+19 x^3+50 x^2+78 x+43$
- $y^2=87 x^6+96 x^5+9 x^4+24 x^3+38 x^2+44 x+82$
- $y^2=65 x^6+69 x^5+83 x^4+33 x^3+123 x^2+114 x+19$
- $y^2=73 x^6+41 x^5+52 x^4+111 x^3+x^2+109 x+53$
- $y^2=57 x^6+45 x^5+45 x^4+118 x^3+92 x^2+123 x+116$
- $y^2=40 x^6+111 x^5+9 x^4+26 x^3+22 x^2+86 x+25$
- $y^2=116 x^6+80 x^5+101 x^4+109 x^3+37 x^2+88 x+74$
- $y^2=37 x^6+47 x^5+120 x^4+80 x^3+8 x^2+27 x+110$
- $y^2=95 x^6+26 x^5+73 x^4+109 x^3+9 x^2+26 x+63$
- $y^2=116 x^6+126 x^5+65 x^4+60 x^3+56 x^2+76 x+124$
- $y^2=48 x^6+51 x^5+66 x^4+33 x^3+57 x^2+50 x+120$
- $y^2=49 x^6+123 x^5+62 x^4+62 x^3+101 x^2+84 x+69$
- $y^2=97 x^6+100 x^5+24 x^4+72 x^3+48 x^2+114 x+105$
- $y^2=27 x^6+86 x^5+96 x^4+49 x^3+50 x^2+28 x+99$
- $y^2=71 x^6+24 x^5+74 x^4+8 x^3+76 x^2+22 x+91$
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 4.0.2797389.2. |
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.bl_wk | $2$ | (not in LMFDB) |