Invariants
Base field: | $\F_{157}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 24 x + 157 x^{2} )( 1 - 23 x + 157 x^{2} )$ |
$1 - 47 x + 866 x^{2} - 7379 x^{3} + 24649 x^{4}$ | |
Frobenius angles: | $\pm0.0929086555916$, $\pm0.129963694588$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $18090$ | $595920780$ | $14961168361440$ | $369135308690366400$ | $9099080071499588796450$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $111$ | $24173$ | $3866040$ | $607556929$ | $95389204011$ | $14976079181066$ | $2351243414769927$ | $369145196619968161$ | $57955795574388432120$ | $9099059901337777089893$ |
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 $\F_{157}$.
Endomorphism algebra over $\F_{157}$The isogeny class factors as 1.157.ay $\times$ 1.157.ax 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 |
---|---|---|
2.157.ab_aje | $2$ | (not in LMFDB) |
2.157.b_aje | $2$ | (not in LMFDB) |
2.157.bv_bhi | $2$ | (not in LMFDB) |