Invariants
Base field: | $\F_{137}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 23 x + 137 x^{2} )( 1 - 16 x + 137 x^{2} )$ |
$1 - 39 x + 642 x^{2} - 5343 x^{3} + 18769 x^{4}$ | |
Frobenius angles: | $\pm0.0596181899068$, $\pm0.260462969152$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $12$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $14030$ | $347859820$ | $6611252965760$ | $124101356231776000$ | $2329193819846267117150$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $99$ | $18533$ | $2571120$ | $352285089$ | $48261719739$ | $6611853019826$ | $905824239725763$ | $124097929236364801$ | $17001416402639515440$ | $2329194047623275455093$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=87x^6+22x^5+25x^4+22x^3+20x^2+110x+67$
- $y^2=136x^6+67x^5+119x^4+38x^3+101x^2+18x+53$
- $y^2=67x^6+119x^5+89x^4+x^3+98x^2+23x+120$
- $y^2=52x^6+95x^5+47x^4+70x^3+73x^2+58x+26$
- $y^2=98x^6+22x^5+65x^4+61x^3+70x^2+83x+114$
- $y^2=80x^6+61x^5+100x^4+10x^3+110x^2+93x+44$
- $y^2=110x^5+98x^4+50x^3+56x^2+91x+41$
- $y^2=40x^6+133x^5+76x^4+12x^3+127x^2+109x+24$
- $y^2=131x^6+42x^5+99x^4+41x^3+69x^2+117x+135$
- $y^2=3x^6+6x^5+127x^4+117x^3+37x^2+8x+95$
- $y^2=6x^6+12x^5+22x^4+53x^3+33x^2+79x+86$
- $y^2=113x^6+81x^5+67x^4+84x^3+25x^2+104x+132$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{137}$.
Endomorphism algebra over $\F_{137}$The isogeny class factors as 1.137.ax $\times$ 1.137.aq 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.ah_adq | $2$ | (not in LMFDB) |
2.137.h_adq | $2$ | (not in LMFDB) |
2.137.bn_ys | $2$ | (not in LMFDB) |