Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 27 x + 191 x^{2} )( 1 - 23 x + 191 x^{2} )$ |
$1 - 50 x + 1003 x^{2} - 9550 x^{3} + 36481 x^{4}$ | |
Frobenius angles: | $\pm0.0686610702072$, $\pm0.187132320568$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $24$ |
This isogeny class is not 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $27885$ | $1312965225$ | $48528938755440$ | $1771202484229689225$ | $64615178135059740742125$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $142$ | $35988$ | $6964672$ | $1330867268$ | $254195413202$ | $48551235379038$ | $9273284314651982$ | $1771197286087321348$ | $338298681552776456512$ | $64615048177692355395348$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=183x^6+157x^5+48x^4+111x^3+38x^2+157x+145$
- $y^2=188x^6+144x^5+161x^4+133x^3+35x^2+23x+4$
- $y^2=44x^6+82x^5+162x^4+68x^3+162x^2+82x+44$
- $y^2=172x^6+160x^5+83x^4+52x^3+158x^2+94x+103$
- $y^2=139x^6+62x^5+110x^4+171x^3+110x^2+62x+139$
- $y^2=107x^6+111x^5+186x^4+114x^3+73x^2+32x+148$
- $y^2=132x^6+64x^5+86x^4+143x^3+107x^2+37x+98$
- $y^2=105x^6+117x^5+161x^4+137x^3+51x^2+54x+19$
- $y^2=22x^6+25x^5+66x^4+170x^3+66x^2+25x+22$
- $y^2=42x^6+32x^5+112x^4+141x^3+112x^2+32x+42$
- $y^2=65x^6+23x^5+39x^4+83x^3+173x^2+136x+4$
- $y^2=28x^6+23x^5+66x^4+187x^3+66x^2+23x+28$
- $y^2=148x^6+101x^5+56x^4+141x^3+56x^2+101x+148$
- $y^2=178x^6+103x^5+143x^4+75x^3+143x^2+103x+178$
- $y^2=188x^6+163x^5+20x^4+179x^3+115x^2+26x+186$
- $y^2=160x^6+167x^5+141x^4+145x^3+149x^2+99x+160$
- $y^2=121x^6+25x^5+30x^4+27x^3+30x^2+25x+121$
- $y^2=136x^6+184x^5+95x^4+85x^3+95x^2+184x+136$
- $y^2=60x^6+188x^5+6x^4+150x^3+51x^2+130x+73$
- $y^2=111x^6+112x^5+13x^4+56x^3+36x^2+139x+184$
- $y^2=144x^6+89x^5+128x^4+119x^3+128x^2+89x+144$
- $y^2=163x^6+92x^5+138x^4+135x^3+138x^2+92x+163$
- $y^2=11x^6+110x^5+182x^4+10x^3+3x^2+180x+74$
- $y^2=62x^6+180x^5+43x^4+49x^3+43x^2+180x+62$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{191}$.
Endomorphism algebra over $\F_{191}$The isogeny class factors as 1.191.abb $\times$ 1.191.ax and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.ae_ajf | $2$ | (not in LMFDB) |
2.191.e_ajf | $2$ | (not in LMFDB) |
2.191.by_bmp | $2$ | (not in LMFDB) |