Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 48 x + 951 x^{2} - 9168 x^{3} + 36481 x^{4}$ |
Frobenius angles: | $\pm0.0856585252156$, $\pm0.218971105078$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.13040272.1 |
Galois group: | $D_{4}$ |
Jacobians: | $16$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28217$ | $1316294833$ | $48543204099908$ | $1771241026132892713$ | $64615235944826395314857$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $144$ | $36080$ | $6966720$ | $1330896228$ | $254195640624$ | $48551234577158$ | $9273284257555728$ | $1771197285222884164$ | $338298681550606970688$ | $64615048177915421324240$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=88x^6+22x^5+34x^4+146x^3+58x^2+46x+45$
- $y^2=187x^6+95x^5+44x^4+26x^3+105x^2+145x+55$
- $y^2=61x^6+189x^5+153x^4+29x^3+130x^2+183x+126$
- $y^2=111x^6+121x^5+39x^4+69x^3+13x^2+99x+55$
- $y^2=151x^6+179x^5+74x^4+69x^3+72x^2+85x+152$
- $y^2=89x^6+124x^5+134x^4+188x^3+64x^2+57x+64$
- $y^2=28x^6+105x^5+54x^4+x^3+57x^2+78x+69$
- $y^2=5x^6+22x^5+47x^4+x^3+33x^2+79x+22$
- $y^2=92x^6+72x^5+47x^4+155x^3+153x^2+140x+103$
- $y^2=6x^6+98x^5+117x^4+176x^3+89x^2+88x+145$
- $y^2=85x^6+27x^5+151x^4+38x^3+102x^2+166x+140$
- $y^2=109x^6+73x^5+81x^4+146x^3+45x^2+94x+189$
- $y^2=107x^6+113x^5+160x^4+26x^3+163x^2+87x+111$
- $y^2=171x^6+98x^5+58x^4+182x^3+90x^2+190x+186$
- $y^2=143x^6+47x^5+171x^4+113x^3+46x^2+60x+114$
- $y^2=64x^6+116x^5+7x^4+122x^3+58x^2+119x+94$
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 4.0.13040272.1. |
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.bw_bkp | $2$ | (not in LMFDB) |