Invariants
| Base field: | $\F_{167}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 25 x + 167 x^{2} )( 1 - 24 x + 167 x^{2} )$ |
| $1 - 49 x + 934 x^{2} - 8183 x^{3} + 27889 x^{4}$ | |
| Frobenius angles: | $\pm0.0816525061160$, $\pm0.121023609245$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Cyclic group of points: | no |
| Non-cyclic primes: | $2$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $20592$ | $763057152$ | $21669154917696$ | $604942471009603584$ | $16871931673953589099152$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $119$ | $27357$ | $4652564$ | $777764633$ | $129892014469$ | $21691967376222$ | $3622557720195211$ | $604967119229175121$ | $101029508565351257948$ | $16871927925352056817557$ |
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 $\F_{167}$.
Endomorphism algebra over $\F_{167}$| The isogeny class factors as 1.167.az $\times$ 1.167.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 |
|---|---|---|
| 2.167.ab_akg | $2$ | (not in LMFDB) |
| 2.167.b_akg | $2$ | (not in LMFDB) |
| 2.167.bx_bjy | $2$ | (not in LMFDB) |