Invariants
| Base field: | $\F_{173}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 23 x + 173 x^{2} )( 1 - 22 x + 173 x^{2} )$ |
| $1 - 45 x + 852 x^{2} - 7785 x^{3} + 29929 x^{4}$ | |
| Frobenius angles: | $\pm0.161302001611$, $\pm0.184705758688$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $22952$ | $886222624$ | $26811559478144$ | $802419360182962816$ | $24014026503592729765832$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $129$ | $29609$ | $5178258$ | $895812225$ | $154965303069$ | $26808773397158$ | $4637914534086753$ | $802359179697965089$ | $138808137868420325274$ | $24013807852228366497089$ |
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.ax $\times$ 1.173.aw 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_age | $2$ | (not in LMFDB) |
| 2.173.b_age | $2$ | (not in LMFDB) |
| 2.173.bt_bgu | $2$ | (not in LMFDB) |