Invariants
| Base field: | $\F_{137}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 39 x + 645 x^{2} - 5343 x^{3} + 18769 x^{4}$ |
| Frobenius angles: | $\pm0.0869532210059$, $\pm0.251808753161$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.15131557.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $10$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $14033$ | $347976301$ | $6612157193537$ | $124105066066076341$ | $2329204294369226148608$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $99$ | $18539$ | $2571471$ | $352295619$ | $48261936774$ | $6611856425939$ | $905824282264623$ | $124097929670110243$ | $17001416406443177835$ | $2329194047657402219054$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 10 curves (of which all are hyperelliptic):
- $y^2=62 x^6+60 x^5+31 x^4+68 x^3+12 x^2+4 x+70$
- $y^2=30 x^6+39 x^5+107 x^4+94 x^3+132 x^2+20 x+35$
- $y^2=27 x^6+20 x^5+x^4+130 x^3+18 x^2+87 x+28$
- $y^2=124 x^6+23 x^5+79 x^4+51 x^3+127 x^2+66 x+124$
- $y^2=132 x^6+74 x^5+49 x^4+51 x^3+x^2+110 x+74$
- $y^2=13 x^6+107 x^5+24 x^4+82 x^3+12 x^2+101 x+28$
- $y^2=51 x^6+79 x^5+102 x^4+130 x^3+118 x^2+3 x+67$
- $y^2=97 x^6+59 x^5+51 x^4+45 x^3+134 x^2+56 x+51$
- $y^2=46 x^6+7 x^5+34 x^4+41 x^3+80 x^2+4 x+119$
- $y^2=27 x^6+53 x^5+128 x^4+99 x^3+66 x^2+41 x+15$
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 4.0.15131557.1. |
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 |
|---|---|---|
| 2.137.bn_yv | $2$ | (not in LMFDB) |