Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 48 x + 950 x^{2} - 9168 x^{3} + 36481 x^{4}$ |
Frobenius angles: | $\pm0.0773520389145$, $\pm0.222263726252$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.223488.6 |
Galois group: | $D_{4}$ |
Jacobians: | $56$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28216$ | $1316219968$ | $48542199445624$ | $1771233820354962432$ | $64615199706685581252856$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $144$ | $36078$ | $6966576$ | $1330890814$ | $254195498064$ | $48551231663214$ | $9273284209474800$ | $1771197284582068990$ | $338298681544049898000$ | $64615048177874524561518$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 56 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=175x^6+131x^5+95x^4+29x^3+123x^2+180x+64$
- $y^2=86x^6+26x^5+34x^4+97x^3+59x^2+36x+21$
- $y^2=9x^6+116x^5+79x^4+74x^3+93x^2+95x+26$
- $y^2=179x^6+54x^5+18x^4+60x^3+40x^2+110x+34$
- $y^2=112x^6+104x^5+128x^4+181x^3+92x^2+146x+132$
- $y^2=14x^6+44x^5+10x^4+69x^3+178x^2+47x+70$
- $y^2=21x^6+142x^5+94x^4+179x^3+51x^2+85x+152$
- $y^2=34x^6+190x^5+184x^4+40x^3+174x^2+180x+106$
- $y^2=129x^6+145x^5+166x^4+178x^3+91x^2+84x+68$
- $y^2=14x^6+117x^5+79x^4+30x^3+186x^2+159x+146$
- $y^2=32x^6+49x^5+106x^4+133x^3+58x^2+52x+119$
- $y^2=58x^6+118x^5+98x^4+103x^3+148x^2+10x+74$
- $y^2=34x^6+153x^5+40x^4+28x^3+174x^2+115x+186$
- $y^2=151x^6+41x^5+93x^4+75x^3+7x^2+3x+173$
- $y^2=109x^6+159x^5+43x^4+32x^3+13x^2+108x+171$
- $y^2=97x^6+66x^5+46x^4+14x^3+80x^2+95x+94$
- $y^2=93x^6+144x^5+174x^4+172x^3+73x^2+135x+162$
- $y^2=52x^6+148x^5+171x^4+79x^3+140x^2+103x+151$
- $y^2=168x^6+32x^5+132x^4+x^3+90x^2+64x+134$
- $y^2=176x^6+5x^5+74x^4+116x^3+166x^2+3x+189$
- and 36 more
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 4.0.223488.6. |
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_bko | $2$ | (not in LMFDB) |