Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 48 x + 946 x^{2} - 9168 x^{3} + 36481 x^{4}$ |
Frobenius angles: | $\pm0.0359858559519$, $\pm0.233419945036$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.7488.1 |
Galois group: | $D_{4}$ |
Jacobians: | $62$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28212$ | $1315920528$ | $48538180885428$ | $1771204944078655488$ | $64615053534038868452532$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $144$ | $36070$ | $6966000$ | $1330869118$ | $254194923024$ | $48551219706598$ | $9273284004033648$ | $1771197281572939774$ | $338298681505284405648$ | $64615048177408841404390$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 62 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=40x^6+179x^5+140x^4+61x^3+96x^2+10x+22$
- $y^2=153x^6+173x^5+49x^4+161x^3+183x^2+45x+139$
- $y^2=151x^6+104x^5+128x^4+50x^3+172x^2+175x+59$
- $y^2=166x^6+76x^5+84x^4+98x^3+157x^2+150x+104$
- $y^2=101x^6+2x^5+179x^4+81x^3+60x^2+152x+153$
- $y^2=112x^6+125x^5+108x^4+50x^3+57x^2+27x+82$
- $y^2=159x^6+120x^5+106x^4+100x^3+93x^2+175x+143$
- $y^2=107x^6+135x^5+141x^4+40x^3+101x^2+114x+87$
- $y^2=41x^6+106x^5+79x^4+131x^3+102x^2+36x+167$
- $y^2=92x^6+127x^5+161x^4+31x^3+61x^2+147x+166$
- $y^2=85x^6+89x^5+97x^4+103x^3+55x^2+60x+81$
- $y^2=132x^6+121x^5+181x^4+181x^3+5x^2+127x+99$
- $y^2=108x^6+178x^5+188x^4+149x^3+110x^2+96x+90$
- $y^2=130x^6+138x^5+60x^4+45x^3+138x^2+8x+146$
- $y^2=142x^6+20x^5+70x^4+39x^3+49x^2+30x+121$
- $y^2=142x^6+131x^5+27x^4+53x^3+36x^2+63x+157$
- $y^2=12x^6+106x^5+13x^4+44x^3+26x^2+80x+75$
- $y^2=46x^6+182x^5+131x^4+160x^3+151x^2+68x+74$
- $y^2=121x^6+93x^5+114x^4+75x^3+37x^2+45x+3$
- $y^2=83x^6+179x^5+147x^4+150x^3+62x^2+85x+56$
- and 42 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 4.0.7488.1. |
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_bkk | $2$ | (not in LMFDB) |