Invariants
| Base field: | $\F_{107}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 18 x + 107 x^{2} )( 1 - 17 x + 107 x^{2} )$ |
| $1 - 35 x + 520 x^{2} - 3745 x^{3} + 11449 x^{4}$ | |
| Frobenius angles: | $\pm0.164078095836$, $\pm0.193011390838$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 18 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $8190$ | $128992500$ | $1501333044120$ | $17185541782500000$ | $196721244968829030450$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $73$ | $11265$ | $1225534$ | $131107673$ | $14025952883$ | $1500734953170$ | $160578181710929$ | $17181861907684273$ | $1838459210780173018$ | $196715135689573083825$ |
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.as $\times$ 1.107.ar 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_ado | $2$ | (not in LMFDB) |
| 2.107.b_ado | $2$ | (not in LMFDB) |
| 2.107.bj_ua | $2$ | (not in LMFDB) |