Invariants
Base field: | $\F_{107}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 36 x + 533 x^{2} - 3852 x^{3} + 11449 x^{4}$ |
Frobenius angles: | $\pm0.0666671800057$, $\pm0.224228209066$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1025.1 |
Galois group: | $D_{4}$ |
Jacobians: | $22$ |
Isomorphism classes: | 22 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $8095$ | $128475745$ | $1499936926720$ | $17182698802220025$ | $196716559096562407375$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $72$ | $11220$ | $1224396$ | $131085988$ | $14025618792$ | $1500730738710$ | $160578139501656$ | $17181861616663108$ | $1838459210550747732$ | $196715135722672310100$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 22 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=85x^6+40x^5+82x^4+14x^3+60x^2+77x+50$
- $y^2=54x^6+x^5+23x^4+13x^3+59x^2+98x+54$
- $y^2=58x^6+89x^5+94x^4+78x^3+x^2+66x+103$
- $y^2=7x^6+95x^5+106x^4+92x^3+10x^2+25x+8$
- $y^2=76x^6+33x^5+83x^4+13x^3+62x^2+82x+63$
- $y^2=39x^6+3x^5+106x^4+39x^3+54x^2+27x+17$
- $y^2=43x^6+19x^5+70x^4+94x^3+72x^2+106x+104$
- $y^2=58x^6+97x^5+8x^4+17x^3+63x^2+100x+19$
- $y^2=51x^6+36x^5+x^4+74x^3+89x^2+84x+67$
- $y^2=3x^6+40x^5+11x^4+21x^3+93x^2+44x+22$
- $y^2=30x^6+6x^5+106x^4+48x^3+32x^2+3x+34$
- $y^2=68x^6+69x^5+28x^4+33x^3+93x^2+18x+106$
- $y^2=56x^6+33x^5+98x^4+14x^3+86x^2+97x+57$
- $y^2=77x^6+24x^5+x^4+52x^3+74x^2+27x+69$
- $y^2=71x^6+85x^5+19x^4+61x^3+64x^2+26x+42$
- $y^2=79x^6+2x^5+26x^4+13x^3+47x^2+5x+6$
- $y^2=98x^6+50x^5+33x^4+61x^3+91x^2+73x+93$
- $y^2=19x^6+15x^5+37x^4+53x^3+79x^2+63x+106$
- $y^2=73x^6+21x^5+76x^4+74x^3+8x^2+19x+25$
- $y^2=35x^6+56x^5+60x^4+18x^3+63x^2+87x+56$
- $y^2=x^6+34x^5+25x^4+62x^3+88x^2+88x+104$
- $y^2=91x^6+27x^5+10x^4+93x^3+101x^2+8x+12$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{107}$.
Endomorphism algebra over $\F_{107}$The endomorphism algebra of this simple isogeny class is 4.0.1025.1. |
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 |
---|---|---|
2.107.bk_un | $2$ | (not in LMFDB) |