Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 49 x + 974 x^{2} - 9359 x^{3} + 36481 x^{4}$ |
Frobenius angles: | $\pm0.0443842198615$, $\pm0.213962896348$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1190277.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28048$ | $1314441472$ | $48533475090112$ | $1771202212439569408$ | $64615101848591844452848$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $143$ | $36029$ | $6965324$ | $1330867065$ | $254195113093$ | $48551225690990$ | $9273284111532115$ | $1771197282839151313$ | $338298681512359032740$ | $64615048177329018682949$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=85x^6+184x^5+183x^4+185x^3+162x^2+92x+176$
- $y^2=170x^6+21x^5+107x^4+125x^3+58x^2+187x+73$
- $y^2=38x^6+178x^5+24x^4+149x^3+24x^2+93x+4$
- $y^2=15x^6+109x^5+150x^4+17x^3+60x^2+87x+41$
- $y^2=15x^6+104x^5+142x^4+39x^3+45x^2+27x+72$
- $y^2=45x^6+107x^5+14x^4+10x^3+99x^2+181x+44$
- $y^2=62x^6+178x^5+49x^4+8x^3+159x^2+56x+171$
- $y^2=123x^6+166x^5+131x^4+78x^3+51x^2+103x+108$
- $y^2=14x^6+163x^5+25x^4+140x^3+46x^2+52x+190$
- $y^2=21x^6+85x^5+76x^4+22x^3+45x^2+147x+87$
- $y^2=176x^6+32x^5+122x^4+95x^3+107x^2+75x+19$
- $y^2=81x^6+61x^5+4x^4+185x^3+42x^2+69x+13$
- $y^2=190x^6+55x^5+83x^4+19x^3+33x^2+11x+68$
- $y^2=88x^6+160x^5+56x^4+11x^3+15x^2+99x+146$
- $y^2=45x^6+154x^5+73x^4+84x^3+66x^2+63x+189$
- $y^2=73x^6+128x^5+75x^4+23x^3+166x^2+41x+72$
- $y^2=55x^6+12x^5+125x^4+36x^3+14x^2+22x+134$
- $y^2=73x^6+26x^5+122x^4+20x^3+116x^2+31x+66$
- $y^2=106x^6+159x^5+117x^4+38x^3+35x^2+10x+181$
- $y^2=14x^6+175x^5+102x^4+42x^3+10x^2+20x+106$
- $y^2=146x^6+88x^5+157x^4+27x^3+132x^2+169x+129$
- $y^2=99x^6+72x^5+161x^4+139x^3+92x^2+181x+155$
- $y^2=169x^6+12x^5+60x^4+108x^3+43x^2+170x+16$
- $y^2=122x^6+149x^5+80x^4+121x^3+39x^2+96x+29$
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 4.0.1190277.1. |
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_blm | $2$ | (not in LMFDB) |