Invariants
Base field: | $\F_{157}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 42 x + 742 x^{2} - 6594 x^{3} + 24649 x^{4}$ |
Frobenius angles: | $\pm0.0607074138189$, $\pm0.255796322361$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.137904.1 |
Galois group: | $D_{4}$ |
Jacobians: | $60$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $18756$ | $600717168$ | $14974607060100$ | $369153415717012224$ | $9099063502786454981796$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $116$ | $24370$ | $3869516$ | $607586734$ | $95389030316$ | $14976067785730$ | $2351243178148148$ | $369145193316384094$ | $57955795541366288132$ | $9099059901136920888850$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 60 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=45x^6+124x^5+18x^4+107x^3+91x^2+156x+104$
- $y^2=135x^6+68x^5+121x^4+150x^3+57x^2+97x+48$
- $y^2=52x^6+9x^4+88x^3+137x^2+110x+150$
- $y^2=55x^6+87x^5+46x^4+15x^3+41x^2+40x+113$
- $y^2=143x^6+53x^5+122x^4+126x^3+145x^2+137x+89$
- $y^2=105x^6+124x^5+132x^4+7x^3+102x^2+91x+87$
- $y^2=24x^6+64x^4+57x^3+77x^2+14x+72$
- $y^2=59x^6+122x^5+23x^4+58x^3+70x^2+129x+88$
- $y^2=129x^6+71x^5+91x^4+87x^3+98x^2+134x+23$
- $y^2=70x^6+89x^5+72x^4+129x^3+156x^2+19x+8$
- $y^2=61x^6+143x^5+40x^4+47x^3+99x^2+96x+23$
- $y^2=126x^6+33x^5+33x^4+74x^3+35x^2+12x+156$
- $y^2=38x^6+24x^5+36x^4+85x^3+76x^2+59x+44$
- $y^2=103x^6+23x^5+92x^4+2x^3+130x^2+110x+86$
- $y^2=54x^6+30x^5+83x^4+67x^3+25x^2+143x+2$
- $y^2=143x^6+11x^5+107x^4+51x^3+106x^2+41x$
- $y^2=65x^6+27x^5+82x^4+39x^3+95x^2+6x+112$
- $y^2=139x^6+114x^5+94x^4+88x^3+4x^2+50x+9$
- $y^2=129x^6+35x^5+123x^4+111x^3+127x^2+19x+37$
- $y^2=62x^6+69x^5+58x^4+115x^3+99x^2+93x+148$
- and 40 more
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 4.0.137904.1. |
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 |
---|---|---|
2.157.bq_bco | $2$ | (not in LMFDB) |