Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 49 x + 978 x^{2} - 9359 x^{3} + 36481 x^{4}$ |
Frobenius angles: | $\pm0.0892328849414$, $\pm0.198490921895$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1100801.1 |
Galois group: | $D_{4}$ |
Jacobians: | $24$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28052$ | $1314741136$ | $48537577688912$ | $1771232558340531776$ | $64615261280224090136812$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $143$ | $36037$ | $6965912$ | $1330889865$ | $254195740293$ | $48551239321822$ | $9273284357131091$ | $1771197286583072049$ | $338298681560731593032$ | $64615048177850266351677$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=160x^6+13x^5+36x^4+38x^3+84x^2+99x+55$
- $y^2=15x^6+50x^5+152x^4+141x^3+106x^2+178x+177$
- $y^2=118x^6+168x^5+82x^4+68x^3+62x^2+15x+188$
- $y^2=137x^6+167x^5+140x^4+116x^3+123x^2+43x+78$
- $y^2=14x^6+55x^5+113x^4+167x^3+88x^2+189x+39$
- $y^2=79x^6+85x^5+186x^4+70x^3+33x^2+77$
- $y^2=157x^6+54x^5+177x^4+154x^3+21x^2+50x+179$
- $y^2=31x^6+4x^5+26x^3+102x^2+132x+19$
- $y^2=69x^6+x^5+182x^4+155x^3+37x^2+9x+119$
- $y^2=41x^6+177x^5+44x^4+64x^3+103x^2+118x+72$
- $y^2=89x^6+36x^5+134x^4+124x^3+143x^2+12x+137$
- $y^2=41x^6+122x^5+86x^4+19x^3+177x^2+178x+17$
- $y^2=61x^6+74x^5+28x^4+11x^3+92x^2+159x+142$
- $y^2=48x^6+92x^5+84x^4+160x^3+11x^2+61x+144$
- $y^2=93x^6+23x^5+25x^4+58x^3+141x^2+142x+98$
- $y^2=124x^6+74x^5+22x^4+121x^3+60x^2+16x+67$
- $y^2=98x^6+135x^5+156x^4+156x^3+17x^2+101x+122$
- $y^2=145x^6+81x^5+83x^4+165x^3+82x^2+62x+100$
- $y^2=12x^6+86x^5+108x^4+54x^3+152x^2+150x+179$
- $y^2=160x^6+3x^5+46x^4+11x^3+136x^2+22x+19$
- $y^2=49x^6+181x^5+22x^4+174x^3+116x^2+135x+11$
- $y^2=164x^6+104x^5+116x^4+44x^3+22x^2+141x+111$
- $y^2=63x^6+6x^5+81x^4+x^3+14x^2+119x+181$
- $y^2=114x^6+182x^5+x^4+80x^3+72x^2+129x+17$
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 4.0.1100801.1. |
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 |
---|---|---|
2.191.bx_blq | $2$ | (not in LMFDB) |