Invariants
| Base field: | $\F_{137}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 42 x + 713 x^{2} - 5754 x^{3} + 18769 x^{4}$ |
| Frobenius angles: | $\pm0.0931478584563$, $\pm0.184503139221$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.479808.2 |
| Galois group: | $D_{4}$ |
| Jacobians: | $8$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $13687$ | $345993673$ | $6607972406812$ | $124101769395764889$ | $2329212349354414145287$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $96$ | $18432$ | $2569842$ | $352286260$ | $48262103676$ | $6611862051366$ | $905824370668572$ | $124097930511292900$ | $17001416408792986242$ | $2329194047572379026512$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=63x^6+109x^5+69x^4+56x^3+55x^2+59x+114$
- $y^2=106x^6+108x^5+5x^4+56x^3+80x^2+4x+80$
- $y^2=7x^6+82x^5+97x^4+41x^3+116x^2+28x+99$
- $y^2=66x^6+71x^5+76x^4+49x^3+35x^2+55x+26$
- $y^2=12x^6+56x^5+24x^4+11x^3+105x^2+98x+48$
- $y^2=125x^6+3x^5+42x^4+57x^3+72x^2+46x+124$
- $y^2=123x^6+10x^5+5x^4+127x^3+127x^2+31x+82$
- $y^2=118x^6+124x^5+130x^4+32x^3+79x^2+66x+92$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{137}$.
Endomorphism algebra over $\F_{137}$| The endomorphism algebra of this simple isogeny class is 4.0.479808.2. |
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 |
|---|---|---|
| 2.137.bq_bbl | $2$ | (not in LMFDB) |