Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 49 x + 977 x^{2} - 9359 x^{3} + 36481 x^{4}$ |
Frobenius angles: | $\pm0.0791099210161$, $\pm0.202977754945$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.5519997.1 |
Galois group: | $D_{4}$ |
Jacobians: | $14$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28051$ | $1314666217$ | $48536552030425$ | $1771224979839254125$ | $64615221609140484836656$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $143$ | $36035$ | $6965765$ | $1330884171$ | $254195584228$ | $48551235961367$ | $9273284297855203$ | $1771197285721877731$ | $338298681550827579605$ | $64615048177775117121230$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=154x^6+122x^5+170x^4+123x^3+24x^2+40x+144$
- $y^2=123x^6+57x^5+176x^4+125x^3+69x^2+102x+183$
- $y^2=141x^6+65x^5+23x^4+17x^3+139x^2+53x+188$
- $y^2=187x^6+127x^5+100x^4+150x^3+27x^2+73x+31$
- $y^2=79x^6+58x^5+148x^4+10x^3+163x^2+57x+118$
- $y^2=45x^6+3x^5+171x^4+115x^3+75x^2+3x+46$
- $y^2=148x^6+184x^5+128x^4+3x^3+144x^2+130x+44$
- $y^2=74x^6+82x^5+27x^4+38x^3+92x^2+95x+55$
- $y^2=134x^6+9x^5+32x^4+84x^3+136x^2+41x+135$
- $y^2=168x^6+141x^5+71x^4+171x^3+59x^2+14x+111$
- $y^2=23x^6+84x^5+4x^4+50x^3+154x^2+23x+152$
- $y^2=33x^6+23x^5+153x^4+181x^3+187x^2+152x+98$
- $y^2=2x^6+57x^5+13x^4+171x^3+122x^2+56x+75$
- $y^2=44x^6+138x^5+182x^4+59x^3+44x^2+187x+143$
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 4.0.5519997.1. |
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_blp | $2$ | (not in LMFDB) |