Invariants
Base field: | $\F_{107}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 19 x + 107 x^{2} )( 1 - 18 x + 107 x^{2} )$ |
$1 - 37 x + 556 x^{2} - 3959 x^{3} + 11449 x^{4}$ | |
Frobenius angles: | $\pm0.129482033963$, $\pm0.164078095836$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $0$ |
Isomorphism classes: | 6 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $8010$ | $128176020$ | $1499735657160$ | $17183446433546400$ | $196719426927281726550$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $71$ | $11193$ | $1224230$ | $131091689$ | $14025823261$ | $1500734671506$ | $160578194537167$ | $17181862204379281$ | $1838459214972576050$ | $196715135733805813593$ |
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.at $\times$ 1.107.as 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_aey | $2$ | (not in LMFDB) |
2.107.b_aey | $2$ | (not in LMFDB) |
2.107.bl_vk | $2$ | (not in LMFDB) |