Invariants
| Base field: | $\F_{137}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 39 x + 647 x^{2} - 5343 x^{3} + 18769 x^{4}$ |
| Frobenius angles: | $\pm0.103081824546$, $\pm0.245068145518$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.12390453.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $30$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $14035$ | $348053965$ | $6612760031395$ | $124107532259285925$ | $2329211183281851458800$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $99$ | $18543$ | $2571705$ | $352302619$ | $48262079514$ | $6611858598471$ | $905824307225013$ | $124097929868863411$ | $17001416407022068095$ | $2329194047644567890318$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 30 curves (of which all are hyperelliptic):
- $y^2=95 x^6+113 x^5+5 x^4+7 x^3+62 x^2+129 x+3$
- $y^2=53 x^6+37 x^5+67 x^4+37 x^3+55 x^2+32 x+24$
- $y^2=4 x^6+33 x^5+115 x^4+26 x^3+96 x^2+87 x+48$
- $y^2=127 x^6+13 x^5+75 x^4+3 x^3+127 x^2+3 x+21$
- $y^2=53 x^6+23 x^5+40 x^3+50 x^2+14 x+3$
- $y^2=42 x^6+32 x^5+58 x^4+126 x^3+56 x^2+84 x+27$
- $y^2=115 x^6+133 x^5+110 x^4+59 x^3+52 x^2+81 x+124$
- $y^2=42 x^6+121 x^5+117 x^4+3 x^3+62 x^2+117 x+113$
- $y^2=31 x^6+133 x^5+82 x^4+74 x^3+89 x^2+133 x+6$
- $y^2=83 x^6+130 x^5+44 x^4+36 x^3+71 x^2+18 x+39$
- $y^2=57 x^6+111 x^5+3 x^4+69 x^3+45 x^2+23 x+84$
- $y^2=30 x^6+45 x^5+40 x^4+112 x^3+91 x^2+46 x+132$
- $y^2=98 x^6+35 x^5+127 x^4+133 x^3+29 x^2+57 x+72$
- $y^2=19 x^6+122 x^5+120 x^4+19 x^3+67 x^2+38 x+79$
- $y^2=29 x^6+46 x^5+37 x^4+25 x^3+65 x^2+125 x+81$
- $y^2=20 x^6+91 x^5+52 x^4+121 x^3+133 x^2+87 x+101$
- $y^2=20 x^6+86 x^5+5 x^4+48 x^3+57 x^2+77 x+35$
- $y^2=70 x^6+104 x^5+59 x^4+128 x^3+119 x^2+105 x+5$
- $y^2=20 x^6+6 x^5+18 x^4+36 x^3+33 x^2+46 x+4$
- $y^2=33 x^6+76 x^5+135 x^4+93 x^3+19 x^2+67 x+71$
- $y^2=79 x^6+9 x^5+18 x^4+77 x^3+128 x^2+19 x+114$
- $y^2=30 x^6+59 x^5+48 x^4+64 x^3+51 x^2+114 x+67$
- $y^2=2 x^6+109 x^5+110 x^4+87 x^3+125 x^2+123 x+77$
- $y^2=11 x^6+118 x^5+112 x^4+93 x^3+48 x^2+90 x+55$
- $y^2=47 x^6+124 x^5+124 x^4+87 x^2+127 x+94$
- $y^2=94 x^6+39 x^5+33 x^4+101 x^3+77 x^2+107 x+89$
- $y^2=82 x^6+83 x^5+123 x^4+46 x^3+96 x^2+129 x+8$
- $y^2=29 x^6+42 x^5+110 x^4+17 x^3+44 x^2+133 x+25$
- $y^2=15 x^6+29 x^5+58 x^4+75 x^3+77 x^2+x+52$
- $y^2=134 x^6+77 x^5+10 x^4+26 x^3+46 x^2+20 x+117$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{137}$.
Endomorphism algebra over $\F_{137}$| The endomorphism algebra of this simple isogeny class is 4.0.12390453.1. |
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 |
|---|---|---|
| 2.137.bn_yx | $2$ | (not in LMFDB) |