Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 20 x + 113 x^{2} )( 1 - 19 x + 113 x^{2} )$ |
| $1 - 39 x + 606 x^{2} - 4407 x^{3} + 12769 x^{4}$ | |
| Frobenius angles: | $\pm0.110150159186$, $\pm0.148111132014$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 4 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $8930$ | $159150460$ | $2079591681440$ | $26584862067467200$ | $339460963390899099650$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $75$ | $12461$ | $1441260$ | $163049937$ | $18424581075$ | $2081955861074$ | $235260601594275$ | $26584442505325153$ | $3004041943185781500$ | $339456739029398747261$ |
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.au $\times$ 1.113.at 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_afy | $2$ | (not in LMFDB) |
| 2.113.b_afy | $2$ | (not in LMFDB) |
| 2.113.bn_xi | $2$ | (not in LMFDB) |