Invariants
| Base field: | $\F_{109}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 35 x + 514 x^{2} - 3815 x^{3} + 11881 x^{4}$ |
| Frobenius angles: | $\pm0.0417150322732$, $\pm0.259902228644$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.2898044.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $8546$ | $138838316$ | $1676645756384$ | $19926050676776384$ | $236735589302175372426$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $75$ | $11685$ | $1294680$ | $141161169$ | $15386188975$ | $1677097800426$ | $182803872842715$ | $19925626002422529$ | $2171893276890998040$ | $236736367460711673325$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=3x^6+37x^5+71x^4+64x^3+93x^2+4x+3$
- $y^2=97x^6+71x^5+45x^4+78x^3+62x^2+54x+11$
- $y^2=61x^6+12x^5+94x^4+96x^3+48x^2+98x+72$
- $y^2=75x^6+106x^5+49x^4+84x^3+15x^2+22x+20$
- $y^2=68x^6+51x^5+18x^4+51x^3+97x^2+x+33$
- $y^2=37x^6+12x^5+99x^4+75x^3+69x^2+58x+103$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{109}$.
Endomorphism algebra over $\F_{109}$| The endomorphism algebra of this simple isogeny class is 4.0.2898044.1. |
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 |
|---|---|---|
| 2.109.bj_tu | $2$ | (not in LMFDB) |