Invariants
Base field: | $\F_{193}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 49 x + 983 x^{2} - 9457 x^{3} + 37249 x^{4}$ |
Frobenius angles: | $\pm0.104436197114$, $\pm0.195695727417$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.3479541.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28727$ | $1371398253$ | $51671630448071$ | $1925176757215549509$ | $71709200684399348610032$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $145$ | $36815$ | $7187539$ | $1387526779$ | $267786288850$ | $51682558397735$ | $9974730537999295$ | $1925122954763960179$ | $371548729923022049197$ | $71708904873278633265950$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=143x^6+125x^5+189x^4+28x^3+130x^2+121x+157$
- $y^2=139x^6+116x^5+177x^4+55x^3+83x^2+x+102$
- $y^2=75x^6+139x^5+77x^4+4x^3+140x^2+153x+192$
- $y^2=165x^6+2x^5+4x^4+110x^3+73x^2+131x+37$
- $y^2=53x^6+38x^4+66x^3+190x^2+138x+146$
- $y^2=78x^6+125x^5+83x^4+109x^3+92x^2+127x+34$
- $y^2=25x^6+144x^5+71x^4+185x^3+129x^2+179x+41$
- $y^2=96x^6+41x^5+48x^4+71x^3+125x^2+116x+187$
- $y^2=181x^6+104x^5+150x^4+52x^3+67x^2+11x+6$
- $y^2=83x^6+170x^5+47x^4+142x^3+156x^2+4x+135$
- $y^2=150x^6+168x^5+130x^4+31x^3+75x^2+173x+29$
- $y^2=54x^6+26x^5+73x^4+129x^3+136x^2+173x+73$
- $y^2=162x^6+70x^5+99x^4+172x^3+155x^2+154x+13$
- $y^2=174x^6+93x^5+15x^4+4x^3+75x^2+18x+61$
- $y^2=57x^6+53x^5+181x^4+104x^3+189x^2+103x+180$
- $y^2=3x^6+62x^5+165x^4+31x^3+158x^2+136x+52$
- $y^2=22x^6+147x^5+106x^4+40x^3+104x^2+49x+148$
- $y^2=134x^6+161x^5+180x^4+116x^3+165x^2+114x+165$
- $y^2=150x^6+93x^5+17x^4+25x^3+112x^2+169x+57$
- $y^2=172x^6+156x^5+96x^4+59x^3+147x^2+54x+121$
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 4.0.3479541.1. |
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.bx_blv | $2$ | (not in LMFDB) |