Invariants
Base field: | $\F_{193}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 49 x + 976 x^{2} - 9457 x^{3} + 37249 x^{4}$ |
Frobenius angles: | $\pm0.0246580823525$, $\pm0.221972964900$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.154652.1 |
Galois group: | $D_{4}$ |
Jacobians: | $14$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28720$ | $1370863040$ | $51664223272960$ | $1925121528557561600$ | $71708909058631420711600$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $145$ | $36801$ | $7186510$ | $1387486977$ | $267785199825$ | $51682534943934$ | $9974730121305745$ | $1925122948545500673$ | $371548729845256894030$ | $71708904872483231760961$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=141x^6+143x^5+75x^4+21x^3+37x^2+132x+77$
- $y^2=90x^6+92x^5+166x^4+2x^3+x^2+115x+13$
- $y^2=139x^6+185x^5+138x^4+129x^3+171x^2+185x+153$
- $y^2=130x^6+19x^5+146x^4+182x^3+158x^2+32x+34$
- $y^2=141x^6+37x^5+181x^4+110x^3+59x^2+45x+111$
- $y^2=84x^6+66x^5+96x^4+90x^3+25x^2+129x+184$
- $y^2=13x^6+9x^5+164x^4+21x^3+24x^2+101x+113$
- $y^2=61x^6+55x^5+73x^4+113x^3+149x^2+172x+73$
- $y^2=126x^6+57x^5+166x^4+127x^3+9x^2+28$
- $y^2=17x^6+179x^5+179x^4+9x^3+58x^2+22x+25$
- $y^2=8x^6+118x^5+77x^4+72x^3+82x^2+41x+77$
- $y^2=29x^6+85x^5+143x^4+78x^3+41x^2+46x+187$
- $y^2=106x^6+137x^5+123x^4+42x^3+146x^2+108x+54$
- $y^2=89x^6+12x^5+38x^4+73x^3+51x^2+85x+174$
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 4.0.154652.1. |
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_blo | $2$ | (not in LMFDB) |