Invariants
| Base field: | $\F_{37}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 17 x + 141 x^{2} - 629 x^{3} + 1369 x^{4}$ |
| Frobenius angles: | $\pm0.152758775413$, $\pm0.329514747593$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.1522773.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $8$ |
| Isomorphism classes: | 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $865$ | $1865805$ | $2585606965$ | $3517014437925$ | $4808919212309200$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $21$ | $1363$ | $51045$ | $1876579$ | $69348786$ | $2565723211$ | $94932127017$ | $3512483880931$ | $129961771199025$ | $4808584443632518$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=15x^6+13x^5+21x^4+25x^3+5x^2+36x+19$
- $y^2=9x^6+14x^5+36x^4+5x^3+7x^2+6x+32$
- $y^2=36x^6+22x^5+26x^4+4x^3+17x^2+35x+20$
- $y^2=13x^6+15x^5+16x^4+4x^3+36x^2+23x+31$
- $y^2=24x^5+26x^4+30x^3+8x^2+24x+21$
- $y^2=20x^6+9x^5+35x^4+30x^3+x^2+8x+14$
- $y^2=18x^6+25x^5+13x^4+34x^3+35x^2+31$
- $y^2=7x^6+29x^5+29x^4+34x^3+19x^2+10x+5$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{37}$.
Endomorphism algebra over $\F_{37}$| The endomorphism algebra of this simple isogeny class is 4.0.1522773.1. |
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 |
|---|---|---|
| 2.37.r_fl | $2$ | (not in LMFDB) |