Invariants
| Base field: | $\F_{37}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 10 x + 37 x^{2} )( 1 - 7 x + 37 x^{2} )$ |
| $1 - 17 x + 144 x^{2} - 629 x^{3} + 1369 x^{4}$ | |
| Frobenius angles: | $\pm0.192861133077$, $\pm0.304847772502$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $10$ |
| Isomorphism classes: | 56 |
This isogeny class is not 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $868$ | $1874880$ | $2593431232$ | $3520312185600$ | $4809644273847028$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $21$ | $1369$ | $51198$ | $1878337$ | $69359241$ | $2565728566$ | $94931594373$ | $3512478233953$ | $129961740206886$ | $4808584374285889$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=32x^6+19x^5+14x^3+26x+14$
- $y^2=31x^6+36x^5+24x^4+14x^3+29x^2+12x+2$
- $y^2=4x^6+12x^5+12x^4+7x^3+29x+30$
- $y^2=23x^6+19x^5+30x^4+36x^3+31x^2+30x+22$
- $y^2=31x^6+14x^5+18x^4+35x^3+17x^2+24x+29$
- $y^2=23x^6+5x^5+21x^4+22x^3+16x^2+17x+28$
- $y^2=14x^6+17x^5+6x^4+19x^3+14x^2+31x+13$
- $y^2=35x^6+21x^5+23x^4+7x^3+17x^2+15x+20$
- $y^2=31x^6+4x^5+15x^4+28x^3+18x^2+x+6$
- $y^2=26x^6+3x^5+24x^4+8x^3+32x^2+27x+13$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{37}$.
Endomorphism algebra over $\F_{37}$| The isogeny class factors as 1.37.ak $\times$ 1.37.ah and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
Base change
This is a primitive isogeny class.