Invariants
Base field: | $\F_{131}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 38 x + 610 x^{2} - 4978 x^{3} + 17161 x^{4}$ |
Frobenius angles: | $\pm0.0503250219080$, $\pm0.265216362023$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.630032.3 |
Galois group: | $D_{4}$ |
Jacobians: | $36$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $12756$ | $290683728$ | $5053313240964$ | $86731973658669312$ | $1488374234847193674756$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $94$ | $16938$ | $2247826$ | $294505934$ | $38579417414$ | $5053909251834$ | $662062552545530$ | $86730202745126110$ | $11361656651102164750$ | $1488377021767899881418$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 36 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=74x^6+127x^5+76x^4+27x^3+99x^2+100x+35$
- $y^2=72x^6+25x^5+49x^4+14x^3+54x^2+48x+32$
- $y^2=50x^6+24x^5+97x^4+55x^3+70x^2+19x+76$
- $y^2=13x^6+57x^5+95x^4+91x^3+78x^2+9x+39$
- $y^2=114x^6+31x^5+85x^4+88x^3+68x^2+38x+110$
- $y^2=85x^6+100x^5+87x^4+107x^3+92x^2+23x+56$
- $y^2=84x^6+47x^5+96x^4+100x^3+25x^2+120x+31$
- $y^2=11x^6+70x^5+120x^4+22x^3+67x^2+69x+124$
- $y^2=90x^6+92x^5+14x^4+84x^3+93x^2+44x+8$
- $y^2=24x^6+60x^5+2x^4+56x^3+50x^2+13x+116$
- $y^2=69x^6+105x^5+109x^4+3x^3+88x^2+35x+18$
- $y^2=120x^6+97x^5+38x^4+103x^3+109x^2+83x+37$
- $y^2=73x^6+100x^5+3x^4+107x^3+24x^2+51x+2$
- $y^2=76x^6+124x^5+109x^4+58x^3+128x^2+96x+98$
- $y^2=130x^6+97x^5+16x^4+100x^3+23x^2+72x+82$
- $y^2=63x^6+52x^5+89x^4+59x^3+67x^2+22x+12$
- $y^2=25x^6+110x^5+123x^4+71x^3+90x^2+96x+116$
- $y^2=104x^6+3x^5+121x^4+92x^3+106x^2+27x+61$
- $y^2=97x^6+13x^5+51x^4+28x^3+9x^2+17x+42$
- $y^2=118x^6+79x^5+95x^4+60x^3+8x^2+12x+102$
- and 16 more
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{131}$.
Endomorphism algebra over $\F_{131}$The endomorphism algebra of this simple isogeny class is 4.0.630032.3. |
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 |
---|---|---|
2.131.bm_xm | $2$ | (not in LMFDB) |