Invariants
| Base field: | $\F_{137}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 40 x + 671 x^{2} - 5480 x^{3} + 18769 x^{4}$ |
| Frobenius angles: | $\pm0.121229875658$, $\pm0.215031711367$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.2336400.6 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $13921$ | $347482081$ | $6612065221444$ | $124109271764841481$ | $2329221605166017932561$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $98$ | $18512$ | $2571434$ | $352307556$ | $48262295458$ | $6611862769238$ | $905824358859154$ | $124097930219540548$ | $17001416405406837338$ | $2329194047553271884272$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=62x^6+128x^5+64x^4+8x^3+84x^2+121x+48$
- $y^2=77x^6+44x^5+25x^4+47x^3+12x^2+115x+65$
- $y^2=73x^6+19x^5+54x^4+126x^3+55x^2+39x+5$
- $y^2=25x^6+110x^5+62x^4+17x^3+25x^2+49x+6$
- $y^2=123x^6+110x^5+9x^4+63x^3+76x^2+30x+24$
- $y^2=117x^6+42x^5+118x^3+125x^2+60x+53$
- $y^2=126x^6+53x^5+72x^4+84x^3+73x^2+86x+72$
- $y^2=118x^6+74x^5+19x^4+73x^3+125x^2+31x+41$
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 4.0.2336400.6. |
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.bo_zv | $2$ | (not in LMFDB) |