Invariants
| Base field: | $\F_{107}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 20 x + 107 x^{2} )( 1 - 19 x + 107 x^{2} )$ |
| $1 - 39 x + 594 x^{2} - 4173 x^{3} + 11449 x^{4}$ | |
| Frobenius angles: | $\pm0.0823304377774$, $\pm0.129482033963$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $7832$ | $127316992$ | $1497867399776$ | $17180497637822464$ | $196715709548079020552$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $69$ | $11117$ | $1222704$ | $131069193$ | $14025558219$ | $1500732178022$ | $160578177921321$ | $17181862184132881$ | $1838459216636668368$ | $196715135769650623757$ |
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 $\F_{107}$.
Endomorphism algebra over $\F_{107}$| The isogeny class factors as 1.107.au $\times$ 1.107.at 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 |
|---|---|---|
| 2.107.ab_agk | $2$ | (not in LMFDB) |
| 2.107.b_agk | $2$ | (not in LMFDB) |
| 2.107.bn_ww | $2$ | (not in LMFDB) |