Invariants
Base field: | $\F_{167}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 44 x + 812 x^{2} - 7348 x^{3} + 27889 x^{4}$ |
Frobenius angles: | $\pm0.105104311096$, $\pm0.226940842313$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.11559168.1 |
Galois group: | $D_{4}$ |
Jacobians: | $28$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $21310$ | $769163140$ | $21691760488270$ | $604997958958810000$ | $16872020792281284033550$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $124$ | $27578$ | $4657420$ | $777835974$ | $129892700564$ | $21691969235066$ | $3622557634741988$ | $604967117024683966$ | $101029508532398963260$ | $16871927925013386120218$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=111x^6+134x^5+89x^4+164x^3+150x^2+88x+160$
- $y^2=127x^6+22x^5+102x^4+32x^3+155x^2+16x+156$
- $y^2=99x^6+3x^5+101x^4+100x^3+25x^2+48x+17$
- $y^2=57x^6+112x^5+155x^4+159x^3+105x^2+145x+55$
- $y^2=26x^6+74x^5+27x^4+57x^3+138x^2+34x+29$
- $y^2=2x^6+13x^5+141x^4+162x^3+117x^2+160x+30$
- $y^2=101x^6+134x^5+32x^4+124x^3+96x^2+75x+45$
- $y^2=145x^6+136x^5+128x^4+136x^3+24x^2+6x+21$
- $y^2=83x^6+84x^5+114x^4+77x^3+32x^2+119x+35$
- $y^2=10x^6+103x^5+16x^4+88x^3+33x^2+149x+89$
- $y^2=119x^5+162x^4+94x^3+143x^2+90x+113$
- $y^2=67x^6+20x^5+10x^4+105x^3+15x^2+71x+131$
- $y^2=144x^6+12x^5+119x^4+121x^3+12x^2+25x+37$
- $y^2=30x^6+13x^5+50x^4+117x^3+x^2+51x+39$
- $y^2=32x^6+14x^5+89x^4+3x^3+28x^2+40$
- $y^2=132x^6+64x^5+158x^4+81x^3+104x^2+50x+142$
- $y^2=146x^6+11x^5+153x^4+93x^3+149x^2+21x+156$
- $y^2=6x^6+19x^5+160x^4+100x^3+17x^2+159x+67$
- $y^2=59x^6+76x^5+5x^4+30x^3+48x^2+19x+81$
- $y^2=95x^6+64x^5+28x^4+8x^3+125x^2+104x+76$
- $y^2=124x^6+130x^5+51x^4+123x^3+67x^2+87x+69$
- $y^2=16x^6+78x^5+163x^4+120x^3+161x^2+15$
- $y^2=78x^6+136x^5+141x^4+74x^3+139x^2+45x+140$
- $y^2=78x^6+129x^5+127x^4+159x^3+104x^2+2x+51$
- $y^2=159x^6+32x^5+148x^4+57x^3+149x^2+105x+142$
- $y^2=92x^6+164x^5+50x^4+56x^3+29x^2+93x+49$
- $y^2=94x^6+14x^5+66x^4+131x^3+164x^2+30x+151$
- $y^2=165x^6+148x^5+55x^4+59x^3+116x^2+143x+16$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{167}$.
Endomorphism algebra over $\F_{167}$The endomorphism algebra of this simple isogeny class is 4.0.11559168.1. |
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 |
---|---|---|
2.167.bs_bfg | $2$ | (not in LMFDB) |