Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 21 x + 113 x^{2} )( 1 - 16 x + 113 x^{2} )$ |
| $1 - 37 x + 562 x^{2} - 4181 x^{3} + 12769 x^{4}$ | |
| Frobenius angles: | $\pm0.0498602789898$, $\pm0.228810695365$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $9$ |
| Isomorphism classes: | 59 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $9114$ | $159950700$ | $2080777274856$ | $26585085945600000$ | $339457692681824264394$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $77$ | $12525$ | $1442084$ | $163051313$ | $18424403557$ | $2081951172450$ | $235260524401189$ | $26584441546270753$ | $3004041934022015012$ | $339456738969302980125$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 9 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=84x^6+17x^5+25x^4+81x^3+110x^2+11x+106$
- $y^2=79x^6+102x^5+6x^4+88x^3+40x^2+78x+13$
- $y^2=82x^6+10x^5+28x^4+45x^3+9x^2+82x+48$
- $y^2=43x^6+102x^5+46x^4+23x^3+49x^2+59x+47$
- $y^2=89x^6+81x^5+23x^4+4x^3+37x^2+93x+49$
- $y^2=92x^6+85x^5+34x^4+67x^3+32x^2+73x+27$
- $y^2=7x^6+32x^5+18x^4+102x^3+104x^2+16x+79$
- $y^2=23x^6+85x^5+82x^4+16x^3+9x^2+9x+112$
- $y^2=108x^6+38x^5+89x^4+102x^3+81x^2+108x+50$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{113}$.
Endomorphism algebra over $\F_{113}$| The isogeny class factors as 1.113.av $\times$ 1.113.aq 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.