Invariants
Base field: | $\F_{157}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 45 x + 815 x^{2} - 7065 x^{3} + 24649 x^{4}$ |
Frobenius angles: | $\pm0.0466497743741$, $\pm0.201404606153$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1296981.2 |
Galois group: | $D_{4}$ |
Jacobians: | $10$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $18355$ | $597914125$ | $14967193660015$ | $369144781587703125$ | $9099075010563050520400$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $113$ | $24255$ | $3867599$ | $607572523$ | $95389150958$ | $14976073035015$ | $2351243254374239$ | $369145193685967123$ | $57955795531564635353$ | $9099059900828766708150$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=47x^6+70x^5+132x^4+106x^3+130x^2+77x+52$
- $y^2=20x^6+127x^5+61x^4+64x^3+71x^2+152x+92$
- $y^2=114x^6+137x^5+114x^4+118x^3+27x^2+62x+22$
- $y^2=58x^6+112x^5+38x^4+151x^3+58x^2+12x+71$
- $y^2=132x^6+141x^5+117x^4+93x^3+12x^2+41x+70$
- $y^2=132x^5+38x^4+124x^3+136x^2+122x+61$
- $y^2=60x^6+148x^5+141x^4+69x^3+88x^2+73x+50$
- $y^2=98x^6+119x^5+114x^4+63x^3+32x^2+81x+98$
- $y^2=134x^6+148x^5+154x^4+43x^3+48x^2+101x+43$
- $y^2=24x^6+87x^5+12x^4+59x^3+63x^2+149x+60$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{157}$.
Endomorphism algebra over $\F_{157}$The endomorphism algebra of this simple isogeny class is 4.0.1296981.2. |
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 |
---|---|---|
2.157.bt_bfj | $2$ | (not in LMFDB) |