Invariants
Base field: | $\F_{139}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 41 x + 690 x^{2} - 5699 x^{3} + 19321 x^{4}$ |
Frobenius angles: | $\pm0.0422463462183$, $\pm0.231214793371$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.650133.2 |
Galois group: | $D_{4}$ |
Jacobians: | $16$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $14272$ | $367532544$ | $7209466033408$ | $139355252115843072$ | $2692454435843796503872$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $99$ | $19021$ | $2684472$ | $373305289$ | $51888887709$ | $7212547519270$ | $1002544307487759$ | $139353666182914705$ | $19370159730669954696$ | $2692452204114159428461$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=99x^6+135x^5+74x^4+133x^3+52x^2+9x+118$
- $y^2=63x^6+29x^5+118x^4+128x^3+9x^2+117x+73$
- $y^2=79x^6+105x^5+69x^4+100x^3+24x^2+66x+85$
- $y^2=6x^6+66x^5+134x^4+137x^3+135x^2+66x+88$
- $y^2=114x^6+11x^5+135x^4+107x^3+7x^2+134x+119$
- $y^2=10x^6+70x^5+81x^4+79x^3+39x^2+129x+8$
- $y^2=126x^6+89x^5+16x^4+97x^3+129x^2+126x+63$
- $y^2=6x^5+92x^4+78x^3+61x^2+102x+31$
- $y^2=26x^6+85x^5+67x^4+74x^3+102x^2+116x+118$
- $y^2=15x^6+32x^5+66x^4+16x^3+97x^2+75x+17$
- $y^2=5x^6+63x^5+92x^4+119x^3+57x^2+38x+138$
- $y^2=53x^6+56x^5+74x^4+120x^3+47x^2+84x+118$
- $y^2=52x^6+6x^5+34x^4+123x^3+95x^2+21x+66$
- $y^2=121x^6+18x^5+13x^4+11x^3+6x^2+3x+4$
- $y^2=40x^6+72x^5+13x^4+3x^3+137x^2+40x+23$
- $y^2=30x^6+7x^5+92x^4+57x^3+36x^2+30x+75$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{139}$.
Endomorphism algebra over $\F_{139}$The endomorphism algebra of this simple isogeny class is 4.0.650133.2. |
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 |
---|---|---|
2.139.bp_bao | $2$ | (not in LMFDB) |