Invariants
Base field: | $\F_{193}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 47 x + 923 x^{2} - 9071 x^{3} + 37249 x^{4}$ |
Frobenius angles: | $\pm0.0526881694498$, $\pm0.250841491310$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.30262893.1 |
Galois group: | $D_{4}$ |
Jacobians: | $26$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $29055$ | $1374040005$ | $51676117079535$ | $1925144786215617525$ | $71708910713168138108400$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $147$ | $36887$ | $7188165$ | $1387503739$ | $267785206002$ | $51682532469959$ | $9974730102163281$ | $1925122949467230931$ | $371548729883636735175$ | $71708904873338269761182$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 26 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=12x^6+86x^5+27x^4+72x^3+36x^2+124x+42$
- $y^2=167x^6+85x^5+51x^4+8x^3+122x^2+15x+183$
- $y^2=82x^6+106x^5+112x^4+115x^3+89x^2+64x+21$
- $y^2=155x^6+85x^5+9x^4+133x^3+105x^2+103x+119$
- $y^2=39x^6+18x^5+38x^4+132x^3+150x^2+131x+160$
- $y^2=181x^6+43x^5+176x^4+50x^3+165x^2+126x+17$
- $y^2=104x^6+116x^5+190x^4+14x^3+34x^2+125x+160$
- $y^2=80x^6+54x^5+23x^4+155x^3+184x^2+13x+119$
- $y^2=66x^6+59x^5+158x^4+123x^3+112x^2+8x+57$
- $y^2=20x^6+162x^5+24x^4+168x^3+4x^2+152x+130$
- $y^2=170x^6+53x^5+167x^4+125x^3+168x^2+151x+103$
- $y^2=163x^6+143x^5+11x^4+149x^3+10x^2+10x+41$
- $y^2=88x^6+79x^5+30x^4+20x^3+86x^2+117x+22$
- $y^2=76x^6+145x^5+96x^4+8x^3+185x^2+74x+123$
- $y^2=81x^6+47x^5+185x^4+73x^3+36x^2+35x+21$
- $y^2=100x^6+184x^5+97x^4+177x^3+155x^2+28x+192$
- $y^2=102x^6+142x^5+2x^4+36x^3+20x^2+58x+29$
- $y^2=92x^6+125x^5+119x^4+177x^3+146x^2+150x+36$
- $y^2=58x^6+76x^5+119x^4+50x^3+52x^2+100x+117$
- $y^2=19x^6+132x^5+133x^4+127x^3+123x^2+80x+180$
- $y^2=89x^6+140x^5+99x^4+124x^3+172x^2+115x+160$
- $y^2=136x^6+39x^5+161x^4+89x^3+65x^2+129x+37$
- $y^2=14x^6+154x^5+6x^4+188x^3+87x^2+70x+150$
- $y^2=149x^6+15x^5+92x^4+88x^3+117x^2+125x+102$
- $y^2=92x^6+160x^5+151x^4+149x^3+121x^2+40x+33$
- $y^2=111x^6+90x^5+98x^4+14x^3+118x^2+12x+86$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{193}$.
Endomorphism algebra over $\F_{193}$The endomorphism algebra of this simple isogeny class is 4.0.30262893.1. |
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 |
---|---|---|
2.193.bv_bjn | $2$ | (not in LMFDB) |