Invariants
| Base field: | $\F_{71}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 + 8 x + 71 x^{2} )( 1 + 9 x + 71 x^{2} )$ |
| $1 + 17 x + 214 x^{2} + 1207 x^{3} + 5041 x^{4}$ | |
| Frobenius angles: | $\pm0.657448017853$, $\pm0.679331255589$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 32 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $6480$ | $26127360$ | $127250585280$ | $646016847114240$ | $3255387437923182000$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $89$ | $5181$ | $355532$ | $25422041$ | $1804309099$ | $128098883358$ | $9095126396389$ | $645753576446161$ | $45848499903587012$ | $3255243554720630901$ |
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 $\F_{71}$.
Endomorphism algebra over $\F_{71}$| The isogeny class factors as 1.71.i $\times$ 1.71.j 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 |
|---|---|---|
| 2.71.ar_ig | $2$ | (not in LMFDB) |
| 2.71.ab_cs | $2$ | (not in LMFDB) |
| 2.71.b_cs | $2$ | (not in LMFDB) |