Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 50 x + 1005 x^{2} - 9550 x^{3} + 36481 x^{4}$ |
Frobenius angles: | $\pm0.0951733851509$, $\pm0.174595285009$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.17984.1 |
Galois group: | $D_{4}$ |
Jacobians: | $9$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $27887$ | $1313115169$ | $48531032081252$ | $1771218413301447401$ | $64615264943018569540927$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $142$ | $35992$ | $6964972$ | $1330879236$ | $254195754702$ | $48551243137462$ | $9273284461693282$ | $1771197288448677828$ | $338298681584509306612$ | $64615048178026173776952$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 9 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=4x^6+104x^5+94x^4+83x^3+42x^2+90x+24$
- $y^2=160x^6+51x^5+144x^4+186x^3+185x^2+182x+73$
- $y^2=41x^6+143x^5+163x^4+127x^3+114x^2+141x+111$
- $y^2=49x^6+113x^5+33x^4+85x^3+162x^2+100x+145$
- $y^2=90x^6+19x^5+70x^4+168x^3+158x^2+4x+148$
- $y^2=33x^6+30x^5+134x^4+109x^3+175x^2+83x+82$
- $y^2=16x^6+120x^5+65x^4+65x^3+132x^2+49x+95$
- $y^2=78x^6+184x^5+57x^4+27x^3+161x^2+127x+136$
- $y^2=73x^6+28x^5+188x^4+18x^3+149x^2+44x+44$
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 4.0.17984.1. |
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.by_bmr | $2$ | (not in LMFDB) |