Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 12 x + 113 x^{2} )( 1 - 11 x + 113 x^{2} )$ |
| $1 - 23 x + 358 x^{2} - 2599 x^{3} + 12769 x^{4}$ | |
| Frobenius angles: | $\pm0.309095034261$, $\pm0.326901256467$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 24 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $10506$ | $165469500$ | $2088796700448$ | $26589876407640000$ | $339453975693819064746$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $91$ | $12957$ | $1447636$ | $163080689$ | $18424201811$ | $2081946298194$ | $235260502404515$ | $26584442016660001$ | $3004041944077303108$ | $339456739052031153357$ |
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.am $\times$ 1.113.al 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_dq | $2$ | (not in LMFDB) |
| 2.113.b_dq | $2$ | (not in LMFDB) |
| 2.113.x_nu | $2$ | (not in LMFDB) |