Invariants
| Base field: | $\F_{173}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 24 x + 173 x^{2} )( 1 - 23 x + 173 x^{2} )$ |
| $1 - 47 x + 898 x^{2} - 8131 x^{3} + 29929 x^{4}$ | |
| Frobenius angles: | $\pm0.134271185755$, $\pm0.161302001611$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $22650$ | $883485900$ | $26800490008800$ | $802389032946072000$ | $24013970554885867223250$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $127$ | $29517$ | $5176120$ | $895778369$ | $154964942027$ | $26808772118634$ | $4637914585387511$ | $802359181315333921$ | $138808137898613561080$ | $24013807852650191361957$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{173}$.
Endomorphism algebra over $\F_{173}$| The isogeny class factors as 1.173.ay $\times$ 1.173.ax and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.ab_ahy | $2$ | (not in LMFDB) |
| 2.173.b_ahy | $2$ | (not in LMFDB) |
| 2.173.bv_bio | $2$ | (not in LMFDB) |