Invariants
Base field: | $\F_{167}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 25 x + 167 x^{2} )( 1 - 21 x + 167 x^{2} )$ |
$1 - 46 x + 859 x^{2} - 7682 x^{3} + 27889 x^{4}$ | |
Frobenius angles: | $\pm0.0816525061160$, $\pm0.198098183086$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $30$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $21021$ | $766783017$ | $21683397271536$ | $604979115521549769$ | $16871994899167536229101$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $122$ | $27492$ | $4655624$ | $777811748$ | $129892501222$ | $21691969028622$ | $3622557655383082$ | $604967117271876676$ | $101029508530428123608$ | $16871927924887584936132$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 30 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=119x^6+78x^5+131x^4+155x^3+131x^2+78x+119$
- $y^2=65x^6+121x^5+65x^4+138x^3+65x^2+121x+65$
- $y^2=130x^6+51x^5+141x^4+41x^3+141x^2+51x+130$
- $y^2=5x^6+88x^5+11x^4+14x^3+11x^2+88x+5$
- $y^2=51x^6+112x^5+35x^4+110x^3+138x^2+77x+163$
- $y^2=126x^6+79x^5+113x^4+134x^3+83x^2+124x+55$
- $y^2=111x^6+47x^5+95x^4+152x^3+65x^2+31x+38$
- $y^2=117x^6+76x^5+115x^4+58x^3+106x^2+74x+52$
- $y^2=152x^6+71x^5+44x^4+109x^3+161x^2+122x+95$
- $y^2=102x^6+32x^5+58x^4+62x^3+50x^2+44x+69$
- $y^2=84x^6+13x^5+33x^4+130x^3+33x^2+13x+84$
- $y^2=120x^6+90x^5+150x^4+153x^3+150x^2+90x+120$
- $y^2=33x^6+42x^5+8x^4+162x^3+8x^2+42x+33$
- $y^2=119x^6+98x^5+118x^4+43x^3+51x^2+132x+101$
- $y^2=7x^6+11x^5+30x^4+97x^3+82x^2+44x+41$
- $y^2=136x^6+39x^5+154x^4+22x^3+154x^2+39x+136$
- $y^2=147x^6+7x^5+115x^4+140x^3+115x^2+7x+147$
- $y^2=12x^6+156x^5+146x^4+158x^3+34x^2+46x+40$
- $y^2=163x^6+84x^5+116x^4+73x^3+116x^2+84x+163$
- $y^2=48x^6+60x^5+149x^4+16x^3+149x^2+60x+48$
- $y^2=67x^6+74x^5+45x^4+75x^3+45x^2+74x+67$
- $y^2=102x^6+82x^5+68x^4+117x^3+50x^2+164x+20$
- $y^2=143x^6+145x^5+51x^4+99x^3+160x^2+105x+39$
- $y^2=15x^6+150x^5+20x^4+52x^3+155x^2+135x+125$
- $y^2=165x^6+91x^5+155x^4+12x^3+155x^2+91x+165$
- $y^2=64x^6+90x^5+79x^4+5x^3+79x^2+90x+64$
- $y^2=82x^6+x^5+57x^4+2x^3+9x^2+45x+146$
- $y^2=96x^6+138x^5+134x^4+117x^3+134x^2+138x+96$
- $y^2=105x^6+46x^5+93x^4+47x^3+133x^2+57x+27$
- $y^2=51x^6+129x^5+91x^4+86x^3+47x^2+133x+67$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{167}$.
Endomorphism algebra over $\F_{167}$The isogeny class factors as 1.167.az $\times$ 1.167.av and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.ae_ahj | $2$ | (not in LMFDB) |
2.167.e_ahj | $2$ | (not in LMFDB) |
2.167.bu_bhb | $2$ | (not in LMFDB) |