Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 36 x + 543 x^{2} - 4068 x^{3} + 12769 x^{4}$ |
| Frobenius angles: | $\pm0.0767197926682$, $\pm0.243129589180$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.4366096.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $6$ |
| Isomorphism classes: | 6 |
This isogeny class is simple and geometrically 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $9209$ | $160393153$ | $2081640116900$ | $26586216166081609$ | $339458847565054347929$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $78$ | $12560$ | $1442682$ | $163058244$ | $18424466238$ | $2081951766470$ | $235260533426766$ | $26584441721894404$ | $3004041937058800506$ | $339456739011755526800$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=62x^6+96x^5+67x^4+92x^3+45x^2+85x+24$
- $y^2=3x^6+34x^5+76x^4+6x^3+12x^2+89x+11$
- $y^2=100x^6+44x^5+87x^4+108x^3+98x^2+60x+108$
- $y^2=91x^6+70x^5+98x^4+76x^3+85x^2+74$
- $y^2=73x^6+51x^5+59x^4+64x^3+56x^2+11x+71$
- $y^2=13x^6+47x^5+89x^4+57x^3+106x^2+8x+43$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{113}$.
Endomorphism algebra over $\F_{113}$| The endomorphism algebra of this simple isogeny class is 4.0.4366096.1. |
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.bk_ux | $2$ | (not in LMFDB) |