Invariants
| Base field: | $\F_{37}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 17 x + 137 x^{2} - 629 x^{3} + 1369 x^{4}$ |
| Frobenius angles: | $\pm0.102403901987$, $\pm0.351888711597$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.2394381.2 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $861$ | $1853733$ | $2575186425$ | $3512514461589$ | $4807787602719696$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $21$ | $1355$ | $50841$ | $1874179$ | $69332466$ | $2565666875$ | $94932194133$ | $3512485747459$ | $129961781641377$ | $4808584502486150$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=14x^6+34x^5+34x^4+27x^3+27x^2+5x+23$
- $y^2=30x^6+13x^5+26x^4+x^3+9x^2+28x+8$
- $y^2=22x^6+4x^5+24x^4+36x^3+x^2+35x+36$
- $y^2=11x^6+4x^5+29x^4+2x^3+21x^2+12x+32$
- $y^2=12x^6+14x^5+36x^4+13x^3+20x^2+21x+15$
- $y^2=8x^6+35x^5+15x^3+5x^2+25x+17$
- $y^2=21x^6+13x^5+14x^4+25x^3+x^2+25x+27$
- $y^2=2x^6+33x^5+22x^4+22x^3+10x^2+12x+23$
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 4.0.2394381.2. |
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 |
|---|---|---|
| 2.37.r_fh | $2$ | (not in LMFDB) |