Invariants
Base field: | $\F_{167}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 24 x + 167 x^{2} )( 1 - 20 x + 167 x^{2} )$ |
$1 - 44 x + 814 x^{2} - 7348 x^{3} + 27889 x^{4}$ | |
Frobenius angles: | $\pm0.121023609245$, $\pm0.218341865198$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $54$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $21312$ | $769277952$ | $21692991917376$ | $605004947275382784$ | $16872048054134815839552$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $124$ | $27582$ | $4657684$ | $777844958$ | $129892910444$ | $21691972905822$ | $3622557682634756$ | $604967117420336446$ | $101029508531846034268$ | $16871927924916411373182$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 54 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=108x^6+62x^5+140x^4+92x^3+140x^2+62x+108$
- $y^2=43x^6+83x^5+28x^4+103x^3+27x^2+71x+136$
- $y^2=128x^6+2x^5+101x^4+22x^3+38x^2+43x+59$
- $y^2=44x^6+32x^5+52x^4+87x^3+52x^2+32x+44$
- $y^2=21x^6+74x^5+61x^4+148x^3+122x^2+129x+1$
- $y^2=52x^6+121x^5+144x^4+161x^3+144x^2+121x+52$
- $y^2=93x^6+120x^5+131x^4+99x^3+131x^2+120x+93$
- $y^2=81x^6+9x^5+46x^4+23x^3+46x^2+9x+81$
- $y^2=86x^6+75x^5+19x^4+87x^3+132x^2+42x+101$
- $y^2=118x^6+52x^5+25x^4+123x^3+56x^2+103x+39$
- $y^2=165x^6+23x^5+127x^4+99x^3+126x^2+6x+22$
- $y^2=90x^6+155x^5+40x^4+72x^3+40x^2+155x+90$
- $y^2=148x^6+112x^5+160x^4+76x^3+113x^2+9x+73$
- $y^2=73x^6+35x^5+33x^4+112x^3+94x^2+141x+114$
- $y^2=100x^6+143x^5+119x^4+163x^3+146x^2+105x+33$
- $y^2=149x^6+63x^5+16x^4+82x^3+16x^2+63x+149$
- $y^2=34x^6+4x^5+151x^4+138x^3+139x^2+37x+157$
- $y^2=22x^6+89x^5+162x^4+19x^3+162x^2+89x+22$
- $y^2=68x^6+81x^5+162x^4+128x^3+70x^2+113x+133$
- $y^2=76x^6+102x^5+19x^4+122x^3+19x^2+102x+76$
- and 34 more
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{167}$.
Endomorphism algebra over $\F_{167}$The isogeny class factors as 1.167.ay $\times$ 1.167.au 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_afq | $2$ | (not in LMFDB) |
2.167.e_afq | $2$ | (not in LMFDB) |
2.167.bs_bfi | $2$ | (not in LMFDB) |