Invariants
| Base field: | $\F_{151}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 41 x + 713 x^{2} - 6191 x^{3} + 22801 x^{4}$ |
| Frobenius angles: | $\pm0.0927082729584$, $\pm0.248522595024$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.20399469.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $17283$ | $514117401$ | $11854618115697$ | $270295383549571821$ | $6162704742192021086448$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $111$ | $22547$ | $3443157$ | $519913195$ | $78503067036$ | $11853912990647$ | $1789940630159163$ | $270281037803806819$ | $40812436758878728317$ | $6162677950482337799102$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 26 curves (of which all are hyperelliptic):
- $y^2=48 x^6+70 x^5+23 x^4+116 x^3+60 x^2+130 x+120$
- $y^2=52 x^6+115 x^5+106 x^4+87 x^3+19 x^2+49 x+45$
- $y^2=83 x^6+73 x^5+28 x^4+114 x^3+115 x^2+28 x+131$
- $y^2=79 x^6+28 x^5+107 x^4+121 x^3+27 x^2+7 x+113$
- $y^2=149 x^6+95 x^5+28 x^4+29 x^3+21 x^2+41 x$
- $y^2=46 x^6+82 x^5+132 x^4+57 x^3+73 x^2+132 x+137$
- $y^2=81 x^6+55 x^5+17 x^4+8 x^3+90 x^2+58 x+45$
- $y^2=3 x^6+98 x^5+94 x^4+40 x^3+x^2+147 x+79$
- $y^2=54 x^6+51 x^5+107 x^4+82 x^3+44 x^2+111 x+148$
- $y^2=16 x^6+2 x^5+83 x^4+135 x^3+17 x^2+88 x+100$
- $y^2=114 x^6+129 x^5+24 x^4+93 x^3+22 x^2+27 x+104$
- $y^2=117 x^6+141 x^5+103 x^4+54 x^3+107 x^2+94 x+128$
- $y^2=79 x^6+120 x^5+85 x^4+73 x^3+93 x^2+47 x+82$
- $y^2=98 x^6+87 x^5+81 x^4+68 x^3+31 x^2+73 x+102$
- $y^2=55 x^6+122 x^5+117 x^4+96 x^3+66 x^2+58 x+111$
- $y^2=132 x^6+81 x^5+111 x^4+54 x^3+91 x^2+94 x+89$
- $y^2=27 x^6+32 x^5+135 x^4+67 x^3+43 x^2+108 x+133$
- $y^2=18 x^6+124 x^5+125 x^4+22 x^3+21 x^2+10 x+55$
- $y^2=101 x^6+80 x^5+107 x^4+15 x^3+143 x^2+23 x+135$
- $y^2=46 x^6+124 x^5+44 x^4+117 x^3+44 x^2+75 x+111$
- $y^2=96 x^6+59 x^5+90 x^4+89 x^3+59 x^2+15 x+126$
- $y^2=65 x^6+18 x^5+27 x^4+82 x^3+47 x^2+13 x+148$
- $y^2=147 x^6+8 x^5+36 x^4+98 x^3+65 x^2+65 x+63$
- $y^2=55 x^6+49 x^5+16 x^4+134 x^3+29 x^2+122 x+60$
- $y^2=124 x^6+112 x^5+52 x^4+147 x^3+137 x^2+92 x+99$
- $y^2=8 x^6+71 x^5+144 x^4+137 x^3+123 x^2+26 x+7$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{151}$.
Endomorphism algebra over $\F_{151}$| The endomorphism algebra of this simple isogeny class is 4.0.20399469.1. |
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 |
|---|---|---|
| 2.151.bp_bbl | $2$ | (not in LMFDB) |