Invariants
Base field: | $\F_{163}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 44 x + 807 x^{2} - 7172 x^{3} + 26569 x^{4}$ |
Frobenius angles: | $\pm0.120308870982$, $\pm0.208123667354$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.3084048.5 |
Galois group: | $D_{4}$ |
Jacobians: | $16$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $20161$ | $697429473$ | $18754613236132$ | $498341641315918569$ | $13239737876475551224201$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $120$ | $26248$ | $4330572$ | $705954580$ | $115064502720$ | $18755381286574$ | $3057125353418592$ | $498311415020684260$ | $81224760534660895092$ | $13239635966980342284088$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=136x^6+115x^5+94x^4+25x^3+86x^2+106x+77$
- $y^2=135x^6+161x^5+98x^4+73x^3+139x^2+15x+154$
- $y^2=51x^6+151x^5+19x^4+64x^3+133x^2+90x+130$
- $y^2=120x^6+45x^5+55x^4+108x^3+30x^2+8x+68$
- $y^2=159x^6+62x^5+81x^4+22x^3+142x^2+37x+117$
- $y^2=98x^6+133x^5+9x^4+93x^3+21x^2+131x+98$
- $y^2=144x^6+64x^5+151x^4+118x^3+63x^2+120x+137$
- $y^2=133x^6+16x^5+144x^4+40x^3+17x^2+161x+105$
- $y^2=82x^6+141x^5+61x^4+68x^3+9x^2+93x+63$
- $y^2=106x^6+13x^5+27x^4+6x^3+44x^2+9x+18$
- $y^2=156x^6+5x^5+133x^4+84x^3+131x^2+71x+71$
- $y^2=140x^6+110x^5+37x^4+108x^3+121x^2+30x+12$
- $y^2=32x^6+120x^5+31x^4+77x^3+127x^2+110x+130$
- $y^2=107x^6+153x^5+107x^4+113x^3+86x^2+6x+120$
- $y^2=16x^6+35x^5+132x^4+69x^3+81x^2+10x+2$
- $y^2=71x^6+65x^5+84x^4+116x^3+15x^2+65x+96$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{163}$.
Endomorphism algebra over $\F_{163}$The endomorphism algebra of this simple isogeny class is 4.0.3084048.5. |
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 |
---|---|---|
2.163.bs_bfb | $2$ | (not in LMFDB) |