Invariants
Base field: | $\F_{137}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 40 x + 668 x^{2} - 5480 x^{3} + 18769 x^{4}$ |
Frobenius angles: | $\pm0.0914703999019$, $\pm0.230187862161$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.6084864.2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $13918$ | $347365444$ | $6611137641646$ | $124105337760005776$ | $2329210080181838052718$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $98$ | $18506$ | $2571074$ | $352296390$ | $48262056658$ | $6611858912522$ | $905824311389074$ | $124097929817530174$ | $17001416404541246498$ | $2329194047600197425386$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=128x^6+136x^5+17x^4+131x^3+118x^2+94x+4$
- $y^2=98x^6+49x^5+127x^4+67x^3+8x^2+64x+130$
- $y^2=110x^6+66x^5+45x^4+63x^3+85x^2+12x+71$
- $y^2=77x^6+20x^5+x^4+9x^3+34x^2+2x+114$
- $y^2=27x^6+35x^5+122x^4+8x^3+14x^2+104x+26$
- $y^2=122x^6+19x^5+94x^4+58x^3+3x^2+71x+97$
- $y^2=106x^6+115x^5+19x^3+50x^2+106x+20$
- $y^2=61x^6+105x^5+121x^4+28x^3+30x^2+104x+71$
- $y^2=132x^6+136x^5+94x^4+91x^3+11x^2+75x+113$
- $y^2=131x^6+68x^5+73x^4+120x^3+50x^2+115x+26$
- $y^2=117x^6+128x^5+85x^4+131x^3+118x^2+106x+79$
- $y^2=27x^6+4x^5+69x^4+129x^3+94x^2+124x+19$
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 4.0.6084864.2. |
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.bo_zs | $2$ | (not in LMFDB) |