Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 47 x + 925 x^{2} - 8977 x^{3} + 36481 x^{4}$ |
Frobenius angles: | $\pm0.0900686723414$, $\pm0.234746497408$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.28164437.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28383$ | $1317851073$ | $48548936755053$ | $1771251341770094877$ | $64615227433446386854608$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $145$ | $36123$ | $6967543$ | $1330903979$ | $254195607140$ | $48551231988999$ | $9273284211065369$ | $1771197284883884035$ | $338298681555534856459$ | $64615048178127944533518$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 62 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=23x^6+142x^5+19x^4+159x^3+55x^2+85x+189$
- $y^2=42x^6+82x^5+62x^4+57x^3+39x^2+85x+53$
- $y^2=153x^6+169x^5+66x^4+75x^3+48x^2+48x+189$
- $y^2=20x^6+151x^4+40x^3+138x^2+157x+186$
- $y^2=89x^6+52x^5+137x^3+74x^2+159x+68$
- $y^2=133x^6+156x^5+22x^4+118x^3+23x^2+75x+161$
- $y^2=184x^6+11x^5+23x^4+82x^3+69x^2+96x+11$
- $y^2=86x^6+128x^5+38x^4+45x^3+85x^2+54x+52$
- $y^2=181x^6+9x^5+169x^4+173x^3+92x^2+96x+129$
- $y^2=76x^6+144x^5+2x^4+100x^3+40x^2+37x+155$
- $y^2=104x^6+145x^5+76x^4+53x^3+19x^2+23x+49$
- $y^2=48x^6+71x^5+30x^4+163x^3+55x^2+127x+132$
- $y^2=94x^6+112x^5+176x^4+72x^3+48x^2+186x+130$
- $y^2=94x^6+75x^5+154x^4+155x^3+154x^2+142x+160$
- $y^2=132x^6+103x^5+167x^4+82x^3+118x^2+136x+13$
- $y^2=113x^6+41x^5+78x^4+61x^3+174x^2+184x+140$
- $y^2=116x^6+38x^5+118x^4+26x^3+45x^2+151x+7$
- $y^2=141x^6+85x^5+122x^4+37x^3+117x^2+83x+112$
- $y^2=70x^6+113x^5+6x^4+135x^3+63x^2+111x+140$
- $y^2=174x^6+57x^5+77x^4+108x^3+150x^2+60x+114$
- 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 4.0.28164437.1. |
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.bv_bjp | $2$ | (not in LMFDB) |