Invariants
Base field: | $\F_{137}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 21 x + 137 x^{2} )( 1 - 18 x + 137 x^{2} )$ |
$1 - 39 x + 652 x^{2} - 5343 x^{3} + 18769 x^{4}$ | |
Frobenius angles: | $\pm0.145687313345$, $\pm0.220793476886$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $36$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $14040$ | $348248160$ | $6614267194080$ | $124113673139414400$ | $2329228076205097618200$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $99$ | $18553$ | $2572290$ | $352320049$ | $48262429539$ | $6611863686766$ | $905824357825563$ | $124097930056017121$ | $17001416401942187250$ | $2329194047499778932793$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 36 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=29x^6+136x^5+49x^4+21x^3+99x^2+81x+43$
- $y^2=38x^6+61x^5+88x^4+60x^3+14x^2+28x+42$
- $y^2=129x^6+21x^5+55x^4+100x^3+15x^2+53x+133$
- $y^2=49x^6+93x^5+114x^4+22x^3+133x^2+103x+69$
- $y^2=62x^6+56x^5+87x^4+125x^3+127x^2+34x+79$
- $y^2=19x^6+29x^5+2x^4+102x^3+105x^2+67x+60$
- $y^2=55x^6+133x^5+32x^4+9x^3+52x^2+15x+47$
- $y^2=24x^6+10x^5+83x^4+101x^3+6x^2+50x+60$
- $y^2=88x^6+99x^5+121x^4+123x^3+47x^2+59x+116$
- $y^2=72x^6+36x^5+122x^4+58x^3+126x^2+47x+113$
- $y^2=136x^6+114x^5+67x^4+8x^3+71x^2+56x+71$
- $y^2=11x^6+20x^5+115x^4+94x^3+113x^2+70x+77$
- $y^2=81x^6+94x^5+12x^4+113x^3+98x^2+45x+90$
- $y^2=53x^6+87x^5+93x^4+126x^3+29x^2+67x+84$
- $y^2=10x^6+83x^5+134x^4+4x^3+123x^2+100x+86$
- $y^2=78x^6+2x^5+105x^4+105x^3+54x^2+94x+124$
- $y^2=84x^6+5x^5+90x^4+101x^3+33x^2+64x+102$
- $y^2=11x^6+122x^5+122x^4+70x^3+56x^2+82x+2$
- $y^2=75x^6+83x^5+112x^4+76x^3+25x^2+90x+8$
- $y^2=65x^6+61x^5+131x^4+32x^3+82x^2+136x+18$
- and 16 more
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{137}$.
Endomorphism algebra over $\F_{137}$The isogeny class factors as 1.137.av $\times$ 1.137.as 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 |
---|---|---|
2.137.ad_aea | $2$ | (not in LMFDB) |
2.137.d_aea | $2$ | (not in LMFDB) |
2.137.bn_zc | $2$ | (not in LMFDB) |