Invariants
| Base field: | $\F_{173}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 25 x + 173 x^{2} )( 1 - 24 x + 173 x^{2} )$ |
| $1 - 49 x + 946 x^{2} - 8477 x^{3} + 29929 x^{4}$ | |
| Frobenius angles: | $\pm0.100717649571$, $\pm0.134271185755$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $22350$ | $880634700$ | $26787963241800$ | $802349304553368000$ | $24013871780333827581750$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $125$ | $29421$ | $5173700$ | $895734017$ | $154964304625$ | $26808765149034$ | $4637914542023125$ | $802359181687269793$ | $138808137917606328500$ | $24013807853067786557061$ |
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.az $\times$ 1.173.ay 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_aju | $2$ | (not in LMFDB) |
| 2.173.b_aju | $2$ | (not in LMFDB) |
| 2.173.bx_bkk | $2$ | (not in LMFDB) |