Invariants
| Base field: | $\F_{151}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 22 x + 151 x^{2} )^{2}$ |
| $1 - 44 x + 786 x^{2} - 6644 x^{3} + 22801 x^{4}$ | |
| Frobenius angles: | $\pm0.147055957538$, $\pm0.147055957538$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $24$ |
This isogeny class is not 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $16900$ | $511664400$ | $11849222752900$ | $270294013587686400$ | $6162737219880160562500$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $108$ | $22438$ | $3441588$ | $519910558$ | $78503480748$ | $11853924429958$ | $1789940818358388$ | $270281039895272638$ | $40812436770650937708$ | $6162677950365719936998$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):
- $y^2=33 x^6+60 x^5+149 x^4+78 x^3+53 x^2+6 x+56$
- $y^2=139 x^6+96 x^5+44 x^4+148 x^3+39 x^2+x$
- $y^2=82 x^6+5 x^5+84 x^4+53 x^3+64 x^2+34 x+128$
- $y^2=126 x^6+120 x^5+18 x^4+51 x^3+18 x^2+120 x+126$
- $y^2=17 x^6+106 x^5+91 x^4+71 x^3+91 x^2+106 x+17$
- $y^2=139 x^6+22 x^5+13 x^4+141 x^3+70 x^2+19 x+146$
- $y^2=104 x^6+46 x^5+38 x^4+147 x^3+145 x^2+146 x+48$
- $y^2=18 x^6+47 x^5+2 x^4+136 x^3+139 x^2+31 x+38$
- $y^2=66 x^6+x^5+68 x^4+104 x^2+59 x+132$
- $y^2=7 x^6+146 x^5+126 x^4+150 x^3+138 x^2+59 x+77$
- $y^2=145 x^6+88 x^5+37 x^4+26 x^3+37 x^2+88 x+145$
- $y^2=128 x^6+39 x^5+111 x^4+17 x^3+112 x^2+40 x+128$
- $y^2=37 x^6+53 x^5+9 x^4+105 x^3+144 x^2+39 x+111$
- $y^2=141 x^6+109 x^5+74 x^4+87 x^3+139 x^2+30 x+14$
- $y^2=59 x^6+55 x^4+55 x^2+59$
- $y^2=69 x^6+44 x^5+85 x^4+76 x^3+133 x^2+16 x+132$
- $y^2=6 x^6+6 x^3+56$
- $y^2=140 x^6+126 x^5+39 x^4+31 x^3+39 x^2+126 x+140$
- $y^2=63 x^6+71 x^5+72 x^4+104 x^3+85 x^2+82 x+52$
- $y^2=135 x^6+52 x^4+33 x^3+101 x^2+122 x+1$
- $y^2=107 x^6+44 x^5+58 x^4+99 x^3+58 x^2+44 x+107$
- $y^2=89 x^6+16 x^4+16 x^2+89$
- $y^2=6 x^6+83 x^3+7$
- $y^2=28 x^6+19 x^5+94 x^4+19 x^3+94 x^2+19 x+28$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{151}$.
Endomorphism algebra over $\F_{151}$| The isogeny class factors as 1.151.aw 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-30}) \)$)$ |
Base change
This is a primitive isogeny class.