Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 47 x + 924 x^{2} - 8977 x^{3} + 36481 x^{4}$ |
Frobenius angles: | $\pm0.0832068261027$, $\pm0.237476928001$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.30190760.1 |
Galois group: | $D_{4}$ |
Jacobians: | $20$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28382$ | $1317776260$ | $48547953096200$ | $1771244503379092640$ | $64615194518934045052762$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $145$ | $36121$ | $6967402$ | $1330898841$ | $254195477655$ | $48551229498538$ | $9273284173383025$ | $1771197284444768721$ | $338298681552074787382$ | $64615048178122875610401$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=161x^6+185x^5+36x^4+149x^3+183x^2+55x+118$
- $y^2=76x^6+8x^5+13x^4+64x^3+97x^2+49x+42$
- $y^2=38x^6+172x^5+83x^4+54x^3+82x^2+109x+153$
- $y^2=165x^6+122x^5+23x^4+61x^3+4x^2+83x+156$
- $y^2=19x^6+100x^5+34x^4+162x^3+177x^2+68x+3$
- $y^2=159x^6+134x^5+179x^4+167x^3+6x^2+87x+148$
- $y^2=113x^6+120x^5+50x^4+129x^3+178x^2+64x+16$
- $y^2=76x^6+70x^5+154x^4+90x^3+91x^2+179x+16$
- $y^2=44x^6+142x^5+35x^4+64x^3+129x^2+73x+126$
- $y^2=58x^6+132x^5+54x^4+25x^3+183x^2+153x+160$
- $y^2=106x^6+80x^5+122x^4+81x^3+121x^2+78x+26$
- $y^2=177x^6+148x^5+26x^4+108x^3+159x^2+137x+39$
- $y^2=114x^6+163x^5+168x^4+145x^3+3x^2+175x+91$
- $y^2=186x^6+85x^5+143x^4+135x^3+127x^2+7x+186$
- $y^2=142x^6+106x^5+133x^4+165x^3+131x^2+51x+99$
- $y^2=189x^6+156x^5+151x^4+36x^3+72x^2+5x+154$
- $y^2=34x^6+8x^5+43x^4+110x^3+29x^2+67x+8$
- $y^2=128x^6+5x^5+171x^4+25x^3+14x^2+50x+149$
- $y^2=181x^6+186x^5+123x^4+45x^3+130x^2+45x+152$
- $y^2=127x^6+25x^5+64x^4+84x^3+75x^2+137x+34$
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 4.0.30190760.1. |
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_bjo | $2$ | (not in LMFDB) |