Invariants
Base field: | $\F_{137}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 40 x + 672 x^{2} - 5480 x^{3} + 18769 x^{4}$ |
Frobenius angles: | $\pm0.132371854234$, $\pm0.208023534643$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1159424.1 |
Galois group: | $D_{4}$ |
Jacobians: | $20$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $13922$ | $347520964$ | $6612374422754$ | $124110580288560656$ | $2329225408221710305282$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $98$ | $18514$ | $2571554$ | $352311270$ | $48262374258$ | $6611864013298$ | $905824373197394$ | $124097930312659134$ | $17001416404782209378$ | $2329194047520683008914$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=103x^6+76x^5+66x^4+135x^3+39x^2+42x+21$
- $y^2=70x^6+84x^5+9x^4+41x^3+120x^2+61x+128$
- $y^2=35x^6+53x^5+20x^4+96x^3+70x^2+131x+64$
- $y^2=116x^6+120x^5+132x^4+103x^3+68x^2+39x+116$
- $y^2=83x^6+115x^5+63x^4+133x^3+69x^2+51x+106$
- $y^2=91x^6+8x^5+104x^4+95x^3+60x^2+2x+10$
- $y^2=116x^6+82x^5+28x^4+26x^3+99x^2+123x+45$
- $y^2=61x^6+18x^5+36x^4+123x^3+83x^2+103x+40$
- $y^2=95x^6+112x^5+79x^4+106x^3+80x^2+96x+31$
- $y^2=86x^6+105x^5+18x^4+123x^3+113x^2+26x+93$
- $y^2=35x^6+41x^5+97x^4+40x^3+109x^2+95x+31$
- $y^2=77x^6+11x^5+23x^4+53x^3+10x^2+55x+51$
- $y^2=54x^6+110x^5+41x^4+93x^3+49x^2+15x+16$
- $y^2=112x^6+126x^5+36x^3+92x^2+49x+6$
- $y^2=133x^6+32x^5+115x^4+82x^3+4x^2+14x+117$
- $y^2=92x^6+94x^5+43x^4+45x^3+110x^2+68x+125$
- $y^2=112x^6+39x^5+9x^4+121x^3+57x^2+21x+128$
- $y^2=4x^6+134x^5+58x^4+3x^3+70x^2+11x+58$
- $y^2=113x^6+43x^5+134x^4+103x^3+130x^2+89x+43$
- $y^2=36x^6+28x^5+7x^4+11x^3+126x^2+103x+114$
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 4.0.1159424.1. |
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.bo_zw | $2$ | (not in LMFDB) |