Invariants
| Base field: | $\F_{79}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 16 x + 79 x^{2} )( 1 - 15 x + 79 x^{2} )$ |
| $1 - 31 x + 398 x^{2} - 2449 x^{3} + 6241 x^{4}$ | |
| Frobenius angles: | $\pm0.143514932644$, $\pm0.180303926787$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 8 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4160$ | $37939200$ | $243027249920$ | $1517532337152000$ | $9468816854999652800$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $49$ | $6077$ | $492916$ | $38960953$ | $3077232139$ | $243089302862$ | $19203923706541$ | $1517108893535953$ | $119851596143766364$ | $9468276078858903077$ |
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 $\F_{79}$.
Endomorphism algebra over $\F_{79}$| The isogeny class factors as 1.79.aq $\times$ 1.79.ap 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 |
|---|---|---|
| 2.79.ab_ade | $2$ | (not in LMFDB) |
| 2.79.b_ade | $2$ | (not in LMFDB) |
| 2.79.bf_pi | $2$ | (not in LMFDB) |