Invariants
Base field: | $\F_{131}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 21 x + 131 x^{2} )^{2}$ |
$1 - 42 x + 703 x^{2} - 5502 x^{3} + 17161 x^{4}$ | |
Frobenius angles: | $\pm0.130292526609$, $\pm0.130292526609$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $15$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $12321$ | $288422289$ | $5049386503056$ | $86731547571853209$ | $1488390906522323499201$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $90$ | $16804$ | $2246076$ | $294504484$ | $38579849550$ | $5053920104518$ | $662062720919130$ | $86730204636600004$ | $11361656665987886916$ | $1488377021821170775204$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 15 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=98x^6+119x^5+91x^4+63x^3+91x^2+119x+98$
- $y^2=64x^6+65x^5+62x^4+57x^3+50x^2+24x+82$
- $y^2=61x^6+4x^5+121x^4+101x^3+121x^2+4x+61$
- $y^2=89x^6+10x^5+71x^4+5x^3+71x^2+10x+89$
- $y^2=54x^6+15x^5+38x^4+86x^3+38x^2+15x+54$
- $y^2=42x^6+43x^5+42x^4+99x^3+96x^2+32x+76$
- $y^2=33x^6+32x^5+80x^4+97x^3+45x^2+9x+103$
- $y^2=106x^6+44x^5+52x^4+13x^3+52x^2+44x+106$
- $y^2=63x^6+108x^5+27x^4+110x^3+27x^2+108x+63$
- $y^2=51x^6+44x^5+121x^4+9x^3+113x^2+43x+26$
- $y^2=53x^6+61x^5+66x^4+34x^3+66x^2+61x+53$
- $y^2=64x^6+116x^5+20x^4+101x^3+129x^2+85x+45$
- $y^2=18x^6+20x^5+37x^4+113x^3+37x^2+20x+18$
- $y^2=29x^6+18x^5+13x^4+113x^3+13x^2+18x+29$
- $y^2=93x^6+50x^4+76x^3+50x^2+93$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{131}$.
Endomorphism algebra over $\F_{131}$The isogeny class factors as 1.131.av 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-83}) \)$)$ |
Base change
This is a primitive isogeny class.