Invariants
Base field: | $\F_{139}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 22 x + 139 x^{2} )( 1 - 20 x + 139 x^{2} )$ |
$1 - 42 x + 718 x^{2} - 5838 x^{3} + 19321 x^{4}$ | |
Frobenius angles: | $\pm0.117174211439$, $\pm0.177693164435$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $14160$ | $367027200$ | $7209508790160$ | $139361120450150400$ | $2692480707829065766800$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $98$ | $18994$ | $2684486$ | $373321006$ | $51889394018$ | $7212557867362$ | $1002544467555302$ | $139353668126050846$ | $19370159748397287074$ | $2692452204206655038674$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=94x^6+39x^5+122x^4+94x^3+38x^2+103x+82$
- $y^2=133x^6+23x^5+87x^4+58x^3+94x^2+84x+8$
- $y^2=86x^6+114x^5+20x^4+37x^3+20x^2+114x+86$
- $y^2=85x^6+91x^5+81x^4+115x^3+81x^2+91x+85$
- $y^2=33x^6+27x^5+43x^4+79x^3+43x^2+27x+33$
- $y^2=77x^6+113x^5+38x^4+5x^3+38x^2+113x+77$
- $y^2=72x^6+99x^5+123x^4+95x^3+123x^2+99x+72$
- $y^2=17x^6+59x^5+32x^4+91x^3+26x^2+8x+102$
- $y^2=75x^6+125x^5+94x^4+118x^3+8x^2+52x+76$
- $y^2=59x^6+x^5+91x^4+72x^3+55x^2+116x+23$
- $y^2=134x^6+14x^5+17x^4+26x^3+17x^2+14x+134$
- $y^2=7x^5+68x^4+125x^3+14x^2+131x$
- $y^2=111x^6+22x^5+7x^4+104x^3+83x^2+18x+19$
- $y^2=40x^6+62x^5+46x^4+36x^3+83x^2+17x+58$
- $y^2=64x^6+81x^5+105x^4+23x^3+105x^2+81x+64$
- $y^2=23x^6+129x^5+12x^4+119x^3+12x^2+129x+23$
- $y^2=119x^6+87x^5+121x^4+109x^3+54x^2+88x+123$
- $y^2=73x^6+83x^5+2x^4+x^3+2x^2+83x+73$
- $y^2=25x^6+16x^5+96x^4+86x^3+28x^2+67x+28$
- $y^2=20x^6+99x^5+13x^4+112x^3+13x^2+99x+20$
- $y^2=42x^6+88x^5+43x^4+38x^3+43x^2+88x+42$
- $y^2=69x^6+49x^5+71x^4+7x^3+52x^2+121x+117$
- $y^2=115x^6+138x^5+26x^4+117x^3+126x^2+104x+3$
- $y^2=53x^6+23x^5+69x^4+87x^3+69x^2+23x+53$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{139}$.
Endomorphism algebra over $\F_{139}$The isogeny class factors as 1.139.aw $\times$ 1.139.au 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_agg | $2$ | (not in LMFDB) |
2.139.c_agg | $2$ | (not in LMFDB) |
2.139.bq_bbq | $2$ | (not in LMFDB) |