Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 18 x + 113 x^{2} )( 1 - 17 x + 113 x^{2} )$ |
| $1 - 35 x + 532 x^{2} - 3955 x^{3} + 12769 x^{4}$ | |
| Frobenius angles: | $\pm0.178616545187$, $\pm0.205038125192$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $9312$ | $161023104$ | $2083570913664$ | $26590557364056576$ | $339466447350001288032$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $79$ | $12609$ | $1444018$ | $163084865$ | $18424878719$ | $2081956728798$ | $235260575910383$ | $26584441862139649$ | $3004041933769942354$ | $339456738926992198689$ |
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 $\F_{113}$.
Endomorphism algebra over $\F_{113}$| The isogeny class factors as 1.113.as $\times$ 1.113.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 |
|---|---|---|
| 2.113.ab_adc | $2$ | (not in LMFDB) |
| 2.113.b_adc | $2$ | (not in LMFDB) |
| 2.113.bj_um | $2$ | (not in LMFDB) |