Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 49 x + 975 x^{2} - 9359 x^{3} + 36481 x^{4}$ |
Frobenius angles: | $\pm0.0573856553654$, $\pm0.210617421473$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.5958485.4 |
Galois group: | $D_{4}$ |
Jacobians: | $20$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28049$ | $1314516385$ | $48534500731031$ | $1771209806888796365$ | $64615141893324404297104$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $143$ | $36031$ | $6965471$ | $1330872771$ | $254195270628$ | $48551229145963$ | $9273284175057773$ | $1771197283850101011$ | $338298681526652651681$ | $64615048177515038883726$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=86x^6+108x^5+76x^4+132x^3+150x^2+5x+28$
- $y^2=142x^6+140x^5+22x^4+110x^3+89x^2+176$
- $y^2=79x^6+189x^5+118x^4+42x^3+151x^2+49x+37$
- $y^2=139x^6+14x^5+141x^4+170x^3+167x^2+62x+31$
- $y^2=176x^6+136x^5+13x^4+157x^3+44x^2+129x+45$
- $y^2=131x^6+3x^5+41x^4+41x^3+x^2+175x+172$
- $y^2=102x^6+166x^5+37x^4+144x^3+87x^2+68x+160$
- $y^2=179x^6+101x^5+74x^4+34x^3+109x^2+114x+187$
- $y^2=26x^6+x^5+96x^4+188x^3+86x^2+123x+121$
- $y^2=78x^6+142x^5+155x^4+171x^3+21x^2+55x+47$
- $y^2=145x^6+156x^5+117x^4+142x^3+122x^2+150x+161$
- $y^2=76x^6+8x^5+177x^4+94x^3+41x^2+52x+71$
- $y^2=146x^6+174x^5+129x^4+57x^3+118x^2+84x+22$
- $y^2=127x^6+84x^5+64x^4+47x^3+143x^2+93x+7$
- $y^2=30x^6+89x^5+161x^4+66x^3+126x^2+187x+89$
- $y^2=29x^6+156x^5+49x^4+146x^3+116x^2+80x+14$
- $y^2=85x^6+165x^5+47x^4+184x^3+57x^2+58x+177$
- $y^2=75x^6+19x^5+113x^4+30x^3+82x^2+126x+153$
- $y^2=123x^6+65x^5+33x^4+57x^3+180x^2+125x+41$
- $y^2=127x^6+126x^5+125x^4+33x^3+96x^2+42x+34$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{191}$.
Endomorphism algebra over $\F_{191}$The endomorphism algebra of this simple isogeny class is 4.0.5958485.4. |
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 |
---|---|---|
2.191.bx_bln | $2$ | (not in LMFDB) |