Invariants
Base field: | $\F_{139}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 21 x + 139 x^{2} )( 1 - 19 x + 139 x^{2} )$ |
$1 - 40 x + 677 x^{2} - 5560 x^{3} + 19321 x^{4}$ | |
Frobenius angles: | $\pm0.150285916016$, $\pm0.201746658314$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $24$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $14399$ | $368600001$ | $7214058195344$ | $139370028633106425$ | $2692492625858105380079$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $100$ | $19076$ | $2686180$ | $373344868$ | $51889623700$ | $7212558769526$ | $1002544448153740$ | $139353667550877508$ | $19370159738988717820$ | $2692452204092386759556$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=27x^6+135x^5+24x^4+4x^3+78x^2+62x+82$
- $y^2=96x^6+44x^5+58x^4+115x^3+104x^2+118x+49$
- $y^2=4x^6+51x^5+104x^4+68x^3+19x^2+35x+83$
- $y^2=81x^6+121x^5+121x^4+36x^3+49x^2+106x+117$
- $y^2=18x^6+91x^5+135x^4+74x^3+87x^2+89x+70$
- $y^2=53x^6+40x^5+48x^4+57x^3+126x^2+15x+50$
- $y^2=53x^6+122x^5+26x^4+94x^3+119x^2+36x+53$
- $y^2=21x^6+50x^5+130x^4+46x^3+12x^2+58x+12$
- $y^2=53x^6+135x^5+130x^4+83x^3+10x^2+74x+101$
- $y^2=53x^6+76x^5+130x^4+21x^3+59x^2+88x+135$
- $y^2=118x^6+133x^5+42x^4+18x^3+124x^2+12x+124$
- $y^2=12x^6+32x^5+49x^4+52x^3+24x^2+90x+130$
- $y^2=52x^6+20x^5+89x^4+115x^3+120x^2+4x+64$
- $y^2=9x^6+90x^5+49x^4+2x^3+16x^2+43x+137$
- $y^2=50x^6+67x^5+111x^4+99x^3+115x^2+x+102$
- $y^2=79x^6+94x^5+74x^4+50x^2+128x+79$
- $y^2=28x^6+21x^5+63x^4+79x^3+89x^2+50x+78$
- $y^2=55x^6+97x^5+106x^4+54x^3+5x^2+94x+1$
- $y^2=110x^6+110x^5+100x^4+52x^3+41x^2+134x+130$
- $y^2=27x^6+28x^5+71x^4+124x^3+125x^2+107x+10$
- $y^2=26x^6+84x^5+111x^4+30x^3+48x^2+88x+115$
- $y^2=84x^6+101x^5+109x^4+13x^3+76x^2+2x+39$
- $y^2=15x^6+117x^5+56x^4+120x^3+2x^2+6x+68$
- $y^2=92x^6+77x^5+108x^4+131x^3+103x^2+24x+115$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{139}$.
Endomorphism algebra over $\F_{139}$The isogeny class factors as 1.139.av $\times$ 1.139.at 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 |
---|---|---|
2.139.ac_aer | $2$ | (not in LMFDB) |
2.139.c_aer | $2$ | (not in LMFDB) |
2.139.bo_bab | $2$ | (not in LMFDB) |