Invariants
| Base field: | $\F_{101}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 18 x + 101 x^{2} )( 1 - 17 x + 101 x^{2} )$ |
| $1 - 35 x + 508 x^{2} - 3535 x^{3} + 10201 x^{4}$ | |
| Frobenius angles: | $\pm0.146794250513$, $\pm0.179134577493$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $7140$ | $101959200$ | $1061377878960$ | $10830476947651200$ | $110465698000911928500$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $67$ | $9993$ | $1030162$ | $104078753$ | $10510432127$ | $1061524072278$ | $107213570302787$ | $10828567277388193$ | $1093685273076558442$ | $110462212526570313873$ |
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 $\F_{101}$.
Endomorphism algebra over $\F_{101}$| The isogeny class factors as 1.101.as $\times$ 1.101.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 |
|---|---|---|
| 2.101.ab_aea | $2$ | (not in LMFDB) |
| 2.101.b_aea | $2$ | (not in LMFDB) |
| 2.101.bj_to | $2$ | (not in LMFDB) |