Invariants
| Base field: | $\F_{181}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 46 x + 879 x^{2} - 8326 x^{3} + 32761 x^{4}$ |
| Frobenius angles: | $\pm0.0578498171782$, $\pm0.241355956375$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.1165968.2 |
| Galois group: | $D_{4}$ |
| Jacobians: | $30$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $25269$ | $1061626497$ | $35155826162064$ | $1151954020355506233$ | $37738627935847993326309$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $136$ | $32404$ | $5928730$ | $1073299300$ | $194264404936$ | $35161824770710$ | $6364290790790824$ | $1151936655477088708$ | $208500535043170566514$ | $37738596846946333978324$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 30 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=36x^6+140x^5+160x^4+172x^3+150x^2+12x+6$
- $y^2=14x^6+160x^5+158x^4+72x^3+107x^2+19x+96$
- $y^2=58x^6+45x^5+169x^4+82x^3+47x^2+5x+31$
- $y^2=131x^6+123x^5+141x^4+38x^3+100x^2+134x+139$
- $y^2=75x^6+60x^5+137x^4+120x^3+154x^2+11x+14$
- $y^2=161x^6+50x^5+153x^4+169x^3+74x^2+166x+5$
- $y^2=110x^6+171x^5+46x^4+121x^3+33x^2+154x+68$
- $y^2=100x^6+171x^5+144x^4+165x^3+109x^2+144x+121$
- $y^2=149x^6+37x^5+88x^4+123x^3+78x^2+180x+3$
- $y^2=80x^6+79x^5+15x^4+153x^3+48x^2+161x+116$
- $y^2=61x^6+90x^5+14x^4+92x^3+48x^2+61x+68$
- $y^2=76x^6+69x^5+95x^4+45x^3+179x^2+177x+111$
- $y^2=4x^6+158x^5+47x^4+39x^3+150x^2+13x+173$
- $y^2=105x^6+138x^5+113x^4+166x^3+134x^2+41x+151$
- $y^2=37x^6+126x^5+165x^4+120x^3+4x^2+146x+180$
- $y^2=171x^6+74x^5+89x^4+61x^3+50x^2+15x+89$
- $y^2=44x^6+70x^5+45x^4+78x^3+79x^2+5x+81$
- $y^2=81x^6+30x^5+7x^4+82x^3+96x^2+118x+76$
- $y^2=38x^6+108x^5+28x^4+32x^3+66x^2+62x+146$
- $y^2=47x^6+95x^5+53x^4+107x^3+135x^2+65x+156$
- $y^2=140x^6+100x^5+60x^4+74x^3+107x^2+83x+79$
- $y^2=74x^6+65x^5+129x^4+87x^3+55x^2+125x+69$
- $y^2=134x^6+47x^5+177x^4+77x^3+10x^2+57x+47$
- $y^2=74x^6+28x^5+128x^4+135x^3+120x^2+3x+113$
- $y^2=145x^6+33x^5+66x^4+156x^3+60x^2+55x+24$
- $y^2=180x^6+135x^5+153x^4+171x^3+151x^2+141x+123$
- $y^2=14x^6+88x^5+79x^4+2x^3+116x^2+177x+23$
- $y^2=97x^6+136x^5+120x^4+157x^3+70x^2+21x+69$
- $y^2=165x^6+50x^5+122x^4+135x^3+43x^2+22x+7$
- $y^2=96x^6+68x^5+156x^4+85x^3+97x^2+8x+124$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{181}$.
Endomorphism algebra over $\F_{181}$| The endomorphism algebra of this simple isogeny class is 4.0.1165968.2. |
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 |
|---|---|---|
| 2.181.bu_bhv | $2$ | (not in LMFDB) |