Invariants
| Base field: | $\F_{149}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 41 x + 715 x^{2} - 6109 x^{3} + 22201 x^{4}$ |
| Frobenius angles: | $\pm0.133324076277$, $\pm0.222309508153$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.4105517.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $22$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $16767$ | $487366389$ | $10944836795763$ | $242957892428325477$ | $5393457944198254528272$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $109$ | $21951$ | $3308647$ | $492930779$ | $73440555734$ | $10942535236815$ | $1630436526216719$ | $242935032956872915$ | $36197319877324010581$ | $5393400662024628329286$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 22 curves (of which all are hyperelliptic):
- $y^2=39 x^6+115 x^5+107 x^4+92 x^3+71 x^2+88 x+12$
- $y^2=112 x^6+52 x^5+17 x^4+137 x^3+141 x^2+55 x+26$
- $y^2=101 x^6+29 x^5+17 x^4+55 x^3+57 x^2+92 x+78$
- $y^2=143 x^6+113 x^5+63 x^4+80 x^3+103 x^2+137 x+68$
- $y^2=72 x^6+37 x^5+11 x^4+113 x^3+114 x^2+55 x+100$
- $y^2=17 x^6+118 x^5+52 x^4+82 x^3+80 x^2+145 x+100$
- $y^2=66 x^6+41 x^5+101 x^4+35 x^3+13 x^2+31 x+46$
- $y^2=8 x^6+28 x^5+54 x^4+41 x^3+103 x^2+62 x+10$
- $y^2=34 x^6+21 x^5+53 x^4+70 x^3+125 x^2+55 x+51$
- $y^2=20 x^6+46 x^5+63 x^4+71 x^3+115 x^2+92 x+92$
- $y^2=133 x^6+97 x^5+16 x^4+9 x^3+32 x^2+107 x+10$
- $y^2=135 x^6+47 x^5+84 x^4+121 x^3+115 x^2+70 x+56$
- $y^2=47 x^6+x^4+51 x^3+100 x^2+28 x+28$
- $y^2=13 x^6+135 x^5+7 x^4+70 x^3+122 x^2+38 x+75$
- $y^2=2 x^6+98 x^5+97 x^4+136 x^3+122 x^2+112 x+17$
- $y^2=51 x^6+78 x^5+58 x^4+61 x^3+41 x^2+66 x+65$
- $y^2=147 x^6+104 x^5+58 x^4+22 x^3+129 x^2+135 x+140$
- $y^2=11 x^6+132 x^5+85 x^4+120 x^3+7 x^2+66 x+131$
- $y^2=57 x^6+120 x^5+139 x^4+147 x^3+25 x^2+21 x+37$
- $y^2=31 x^6+5 x^5+107 x^4+114 x^3+48 x^2+36 x+110$
- $y^2=9 x^6+107 x^5+11 x^4+8 x^3+94 x^2+115 x+59$
- $y^2=2 x^6+45 x^5+143 x^4+119 x^3+32 x^2+36 x+23$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{149}$.
Endomorphism algebra over $\F_{149}$| The endomorphism algebra of this simple isogeny class is 4.0.4105517.1. |
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 |
|---|---|---|
| 2.149.bp_bbn | $2$ | (not in LMFDB) |