Invariants
Base field: | $\F_{181}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 49 x + 957 x^{2} - 8869 x^{3} + 32761 x^{4}$ |
Frobenius angles: | $\pm0.0295624989655$, $\pm0.190960746979$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.633717.2 |
Galois group: | $D_{4}$ |
Jacobians: | $8$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $24801$ | $1057440237$ | $35140624323525$ | $1151922971588050725$ | $37738613257322806255056$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $133$ | $32275$ | $5926165$ | $1073270371$ | $194264329378$ | $35161828899307$ | $6364290878494633$ | $1151936656056190051$ | $208500535028375569105$ | $37738596846350067133030$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=180x^6+150x^5+34x^4+137x^3+176x^2+64x+124$
- $y^2=87x^6+63x^5+164x^4+110x^3+4x^2+164x+78$
- $y^2=142x^6+140x^5+2x^4+60x^3+91x^2+144x+119$
- $y^2=58x^6+50x^5+180x^4+32x^3+82x^2+98x+170$
- $y^2=18x^6+143x^5+89x^4+155x^3+149x^2+144x+165$
- $y^2=30x^6+115x^5+76x^4+90x^3+32x^2+89x+61$
- $y^2=35x^6+166x^5+41x^4+84x^3+60x^2+145x+30$
- $y^2=161x^6+26x^5+123x^4+32x^3+50x^2+94x+85$
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 4.0.633717.2. |
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.bx_bkv | $2$ | (not in LMFDB) |