Invariants
| Base field: | $\F_{37}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 + 4 x + 71 x^{2} + 148 x^{3} + 1369 x^{4}$ |
| Frobenius angles: | $\pm0.483096029856$, $\pm0.624722689121$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.1625232.2 |
| Galois group: | $D_{4}$ |
| Jacobians: | $24$ |
| Isomorphism classes: | 24 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1593$ | $2053377$ | $2548373076$ | $3507449228649$ | $4809350278409553$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $42$ | $1496$ | $50310$ | $1871476$ | $69355002$ | $2565751358$ | $94931861682$ | $3512479787044$ | $129961720748142$ | $4808584393087016$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):
- $y^2=5 x^6+x^5+4 x^4+20 x^3+28 x^2+30 x+2$
- $y^2=12 x^6+16 x^5+32 x^4+36 x^3+28 x^2+7 x+26$
- $y^2=21 x^6+17 x^5+12 x^4+2 x^3+34 x^2+28 x+21$
- $y^2=23 x^6+16 x^5+13 x^4+33 x^3+30 x^2+17 x+4$
- $y^2=32 x^6+18 x^5+28 x^4+26 x^3+26 x^2+15 x+1$
- $y^2=22 x^6+8 x^5+29 x^4+21 x^3+14 x^2+36 x+28$
- $y^2=33 x^6+29 x^5+31 x^4+28 x^3+21 x^2+9 x+10$
- $y^2=21 x^6+8 x^5+23 x^4+20 x^3+24 x^2+13 x+4$
- $y^2=20 x^6+18 x^5+9 x^4+3 x^3+16 x^2+27$
- $y^2=31 x^6+13 x^5+2 x^4+26 x^3+21 x^2+30 x+9$
- $y^2=18 x^6+2 x^5+35 x^4+27 x^3+29 x^2+9 x+36$
- $y^2=18 x^6+32 x^5+26 x^4+31 x^3+4 x^2+21 x+5$
- $y^2=31 x^6+7 x^5+9 x^4+34 x^3+11 x^2+7 x+28$
- $y^2=18 x^6+2 x^5+8 x^4+12 x^3+7 x^2+23 x+2$
- $y^2=20 x^6+18 x^5+11 x^4+12 x^3+16 x^2+21 x+12$
- $y^2=4 x^6+24 x^5+31 x^4+21 x^3+27 x^2+2 x+34$
- $y^2=22 x^6+17 x^5+36 x^4+25 x^3+22 x^2+5 x+11$
- $y^2=29 x^6+12 x^5+24 x^4+16 x^3+31 x^2+10 x+36$
- $y^2=35 x^6+12 x^5+29 x^4+24 x^3+26 x^2+14 x+28$
- $y^2=21 x^6+2 x^5+6 x^4+6 x^3+34 x^2+34 x+22$
- $y^2=4 x^6+6 x^5+15 x^4+21 x^3+7 x^2+12 x+11$
- $y^2=23 x^6+3 x^5+26 x^4+4 x^3+8 x^2+x+34$
- $y^2=22 x^6+30 x^5+10 x^4+29 x^3+13 x^2+14 x+36$
- $y^2=13 x^6+5 x^5+24 x^4+15 x^3+32 x^2+16 x+26$
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 4.0.1625232.2. |
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.ae_ct | $2$ | (not in LMFDB) |