Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 27 x + 191 x^{2} )( 1 - 22 x + 191 x^{2} )$ |
$1 - 49 x + 976 x^{2} - 9359 x^{3} + 36481 x^{4}$ | |
Frobenius angles: | $\pm0.0686610702072$, $\pm0.206981219725$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $20$ |
This isogeny class is not 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28050$ | $1314591300$ | $48535526377800$ | $1771217396022016800$ | $64615181813507270343750$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $143$ | $36033$ | $6965618$ | $1330878473$ | $254195427673$ | $48551232569418$ | $9273284237164783$ | $1771197284810948593$ | $338298681539471714798$ | $64615048177663556296473$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=31x^6+159x^5+85x^4+4x^3+59x^2+159x+107$
- $y^2=182x^6+31x^5+96x^4+28x^3+41x^2+189x+185$
- $y^2=55x^6+56x^5+141x^4+118x^3+153x^2+133x+17$
- $y^2=138x^6+46x^5+25x^4+52x^3+48x^2+160x+147$
- $y^2=103x^6+65x^5+96x^4+123x^3+41x^2+75x+30$
- $y^2=162x^6+93x^5+55x^4+180x^3+136x^2+120x+22$
- $y^2=106x^6+75x^5+183x^4+169x^3+142x^2+96x+54$
- $y^2=104x^6+14x^5+34x^4+169x^3+28x^2+22x+97$
- $y^2=137x^6+119x^5+13x^4+121x^3+2x^2+35x+105$
- $y^2=19x^6+157x^5+176x^4+19x^3+33x^2+138x+61$
- $y^2=28x^6+70x^5+69x^4+83x^3+118x^2+116x+37$
- $y^2=178x^6+80x^5+161x^4+162x^3+164x^2+157x+112$
- $y^2=47x^6+166x^5+89x^4+7x^3+18x^2+12x+85$
- $y^2=18x^6+124x^5+16x^4+122x^3+131x^2+47x+105$
- $y^2=43x^6+89x^5+49x^4+110x^3+116x^2+15x+106$
- $y^2=84x^6+161x^5+8x^4+132x^3+121x^2+162x+40$
- $y^2=96x^6+152x^5+111x^4+159x^3+23x^2+113x+26$
- $y^2=42x^6+149x^5+48x^4+97x^3+102x^2+164x+148$
- $y^2=75x^6+52x^5+63x^4+85x^3+43x^2+38x+185$
- $y^2=28x^6+50x^5+28x^4+176x^3+42x^2+17x+73$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{191}$.
Endomorphism algebra over $\F_{191}$The isogeny class factors as 1.191.abb $\times$ 1.191.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.af_aie | $2$ | (not in LMFDB) |
2.191.f_aie | $2$ | (not in LMFDB) |
2.191.bx_blo | $2$ | (not in LMFDB) |