Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 19 x + 113 x^{2} )^{2}$ |
| $1 - 38 x + 587 x^{2} - 4294 x^{3} + 12769 x^{4}$ | |
| Frobenius angles: | $\pm0.148111132014$, $\pm0.148111132014$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $9$ |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $9025$ | $159643225$ | $2080748550400$ | $26586827039355625$ | $339463599592217100625$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $76$ | $12500$ | $1442062$ | $163061988$ | $18424724156$ | $2081957174750$ | $235260608988572$ | $26584442474293828$ | $3004041941456984686$ | $339456738996592992500$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 9 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=77x^6+92x^5+104x^4+42x^3+4x^2+67x+105$
- $y^2=56x^6+90x^5+27x^4+55x^3+108x^2+84x+81$
- $y^2=47x^6+44x^5+21x^4+5x^3+40x^2+15x+66$
- $y^2=35x^6+58x^5+45x^4+8x^3+2x^2+77x+98$
- $y^2=29x^6+99x^5+67x^4+86x^3+83x^2+38x+31$
- $y^2=93x^6+9x^5+102x^4+79x^3+51x^2+87x+54$
- $y^2=41x^6+106x^5+24x^4+85x^3+45x^2+16x+18$
- $y^2=72x^6+103x^5+4x^4+24x^3+87x^2+86x+2$
- $y^2=60x^6+14x^5+96x^4+102x^3+93x^2+53$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{113}$.
Endomorphism algebra over $\F_{113}$| The isogeny class factors as 1.113.at 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-91}) \)$)$ |
Base change
This is a primitive isogeny class.