Invariants
| Base field: | $\F_{173}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 46 x + 865 x^{2} - 7958 x^{3} + 29929 x^{4}$ |
| Frobenius angles: | $\pm0.0332764210250$, $\pm0.228065115178$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.3598400.2 |
| Galois group: | $D_{4}$ |
| Jacobians: | $10$ |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
| $p$-rank: | $1$ |
| Slopes: | $[0, 1/2, 1/2, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $22791$ | $884268009$ | $26799225911964$ | $802361772986057721$ | $24013812478727173114191$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $128$ | $29544$ | $5175878$ | $895747940$ | $154963921948$ | $26808749108478$ | $4637914184473180$ | $802359175749361924$ | $138808137839240445854$ | $24013807852258437897864$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 10 curves (of which all are hyperelliptic):
- $y^2=156 x^6+34 x^5+42 x^4+155 x^3+30 x^2+116 x+171$
- $y^2=110 x^6+48 x^5+95 x^4+41 x^3+104 x^2+21 x+2$
- $y^2=4 x^6+50 x^5+107 x^4+165 x^3+166 x^2+151 x+78$
- $y^2=35 x^6+141 x^5+112 x^4+46 x^3+108 x^2+112 x+126$
- $y^2=11 x^6+129 x^5+98 x^4+115 x^3+142 x^2+139 x+140$
- $y^2=102 x^6+98 x^5+89 x^4+34 x^3+118 x^2+26 x+90$
- $y^2=159 x^6+125 x^5+137 x^4+103 x^3+63 x^2+63 x+123$
- $y^2=33 x^6+15 x^5+148 x^4+108 x^3+108 x^2+34 x+15$
- $y^2=66 x^6+165 x^5+160 x^4+95 x^3+79 x^2+20 x+118$
- $y^2=114 x^6+93 x^5+116 x^4+122 x^3+41 x^2+72 x+33$
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 4.0.3598400.2. |
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_bhh | $2$ | (not in LMFDB) |