Invariants
Base field: | $\F_{137}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 39 x + 641 x^{2} - 5343 x^{3} + 18769 x^{4}$ |
Frobenius angles: | $\pm0.0483327645413$, $\pm0.263061961588$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.10441053.1 |
Galois group: | $D_{4}$ |
Jacobians: | $12$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $14029$ | $347820997$ | $6610951564213$ | $124100116808417829$ | $2329190290697469620224$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $99$ | $18531$ | $2571003$ | $352281571$ | $48261646614$ | $6611851845123$ | $905824224180051$ | $124097929055158339$ | $17001416400566702139$ | $2329194047596845024366$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=130x^6+61x^5+124x^4+93x^3+129x^2+135x+28$
- $y^2=47x^6+60x^5+116x^4+35x^3+33x^2+102x+85$
- $y^2=40x^6+125x^5+114x^4+36x^3+108x^2+107x+102$
- $y^2=61x^6+45x^5+32x^4+85x^3+121x^2+63x+109$
- $y^2=89x^6+128x^5+18x^4+103x^3+37x^2+13x+90$
- $y^2=109x^6+22x^5+68x^4+104x^3+132x^2+75x+104$
- $y^2=75x^6+10x^5+122x^4+93x^3+64x^2+41x+23$
- $y^2=125x^6+30x^5+29x^4+8x^3+85x^2+36x+111$
- $y^2=58x^6+125x^5+134x^4+69x^3+60x^2+108x+133$
- $y^2=132x^6+66x^5+112x^4+21x^3+28x+7$
- $y^2=19x^6+117x^5+117x^4+116x^3+13x^2+39x+80$
- $y^2=107x^6+24x^5+17x^4+97x^3+123x^2+52x+104$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{137}$.
Endomorphism algebra over $\F_{137}$The endomorphism algebra of this simple isogeny class is 4.0.10441053.1. |
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 |
---|---|---|
2.137.bn_yr | $2$ | (not in LMFDB) |