Invariants
Base field: | $\F_{173}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 46 x + 868 x^{2} - 7958 x^{3} + 29929 x^{4}$ |
Frobenius angles: | $\pm0.0714610774504$, $\pm0.218377440981$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.7466816.1 |
Galois group: | $D_{4}$ |
Jacobians: | $24$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $22794$ | $884452788$ | $26801372680650$ | $802375204879051344$ | $24013871929302929582154$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $128$ | $29550$ | $5176292$ | $895762934$ | $154964305588$ | $26808756847470$ | $4637914314309376$ | $802359177621304414$ | $138808137863182853696$ | $24013807852544738922750$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=16x^6+88x^5+46x^4+67x^3+41x^2+88x+44$
- $y^2=26x^6+93x^5+68x^4+16x^3+135x^2+124x+102$
- $y^2=42x^6+82x^5+10x^4+18x^3+151x^2+29x+26$
- $y^2=134x^6+74x^5+42x^4+36x^3+118x^2+159x+2$
- $y^2=63x^6+101x^5+23x^4+91x^3+24x^2+30x+162$
- $y^2=154x^6+73x^5+170x^4+128x^3+93x^2+8x+58$
- $y^2=35x^6+44x^5+152x^4+5x^3+126x^2+3x+70$
- $y^2=5x^6+73x^5+10x^4+145x^3+88x^2+166x+134$
- $y^2=38x^6+62x^5+36x^4+12x^3+167x^2+60x+48$
- $y^2=154x^6+61x^5+147x^4+58x^3+131x^2+67x+94$
- $y^2=109x^6+146x^5+52x^4+7x^3+9x^2+50x+16$
- $y^2=114x^6+101x^5+21x^4+86x^3+111x^2+63x+131$
- $y^2=135x^6+93x^5+168x^4+141x^3+27x^2+68x+66$
- $y^2=36x^6+21x^5+171x^4+129x^3+152x^2+49x+90$
- $y^2=26x^6+77x^5+61x^4+153x^3+87x^2+56x+164$
- $y^2=12x^6+36x^5+161x^4+77x^3+144x^2+106x+33$
- $y^2=168x^6+80x^5+73x^4+152x^3+94x^2+111x+166$
- $y^2=72x^6+63x^5+86x^4+130x^3+81x^2+66x+162$
- $y^2=105x^6+36x^5+159x^4+38x^3+82x^2+149x+137$
- $y^2=25x^6+90x^5+109x^4+154x^3+46x^2+120x+134$
- $y^2=55x^6+97x^5+59x^4+9x^3+107x^2+148x+53$
- $y^2=26x^6+154x^5+81x^4+120x^3+45x^2+3x+107$
- $y^2=8x^6+59x^5+149x^4+132x^3+143x^2+169x+17$
- $y^2=72x^6+33x^5+45x^4+109x^3+168x^2+95x+31$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{173}$.
Endomorphism algebra over $\F_{173}$The endomorphism algebra of this simple isogeny class is 4.0.7466816.1. |
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 |
---|---|---|
2.173.bu_bhk | $2$ | (not in LMFDB) |