Invariants
| Base field: | $\F_{137}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 42 x + 712 x^{2} - 5754 x^{3} + 18769 x^{4}$ |
| Frobenius angles: | $\pm0.0767589501682$, $\pm0.192250456591$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.795456.4 |
| Galois group: | $D_{4}$ |
| Jacobians: | $26$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $13686$ | $345954708$ | $6607647674550$ | $124100287498394064$ | $2329207525064153593446$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $96$ | $18430$ | $2569716$ | $352282054$ | $48262003716$ | $6611860171150$ | $905824341413808$ | $124097930130879934$ | $17001416404766755152$ | $2329194047541632827150$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 26 curves (of which all are hyperelliptic):
- $y^2=90 x^6+119 x^5+59 x^4+33 x^3+26 x^2+70 x+4$
- $y^2=5 x^6+75 x^5+65 x^4+10 x^3+89 x^2+130 x+131$
- $y^2=116 x^6+64 x^5+22 x^4+44 x^3+109 x^2+35 x+33$
- $y^2=58 x^6+103 x^5+15 x^4+89 x^3+91 x^2+23 x+102$
- $y^2=115 x^6+11 x^5+104 x^4+79 x^3+85 x^2+40 x+5$
- $y^2=92 x^6+30 x^5+32 x^4+4 x^3+24 x^2+89 x+38$
- $y^2=104 x^6+30 x^5+115 x^4+66 x^3+55 x^2+36 x+53$
- $y^2=74 x^6+104 x^5+67 x^4+134 x^3+82 x^2+42 x+5$
- $y^2=118 x^6+69 x^5+55 x^4+85 x^3+121 x^2+74 x+97$
- $y^2=23 x^6+13 x^5+14 x^4+95 x^3+102 x^2+7 x+49$
- $y^2=67 x^6+92 x^5+36 x^4+20 x^3+61 x^2+53 x+83$
- $y^2=64 x^6+73 x^5+101 x^4+52 x^3+67 x^2+38 x+44$
- $y^2=85 x^6+42 x^5+19 x^4+46 x^3+39 x^2+86 x+75$
- $y^2=94 x^6+133 x^5+58 x^4+80 x^3+33 x+9$
- $y^2=74 x^6+52 x^5+47 x^4+58 x^3+37 x^2+107 x+83$
- $y^2=99 x^6+15 x^5+29 x^4+44 x^3+65 x^2+134 x+67$
- $y^2=74 x^6+123 x^5+135 x^4+9 x^3+36 x^2+55 x+5$
- $y^2=85 x^6+40 x^5+43 x^4+71 x^3+103 x^2+30 x+96$
- $y^2=126 x^6+113 x^5+38 x^4+81 x^3+130 x^2+55 x+82$
- $y^2=102 x^6+20 x^5+89 x^4+24 x^3+26 x^2+106 x+39$
- $y^2=21 x^6+121 x^5+108 x^4+71 x^3+39 x^2+105 x+12$
- $y^2=46 x^6+30 x^5+88 x^4+46 x^3+38 x^2+114 x+85$
- $y^2=111 x^6+127 x^5+124 x^4+15 x^3+14 x^2+75 x+75$
- $y^2=41 x^6+35 x^5+2 x^4+39 x^3+23 x^2+56 x+16$
- $y^2=67 x^6+63 x^5+114 x^4+125 x^3+39 x^2+59 x+67$
- $y^2=97 x^6+10 x^5+12 x^4+70 x^3+85 x^2+94 x+133$
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 4.0.795456.4. |
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.bq_bbk | $2$ | (not in LMFDB) |