Invariants
Base field: | $\F_{107}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 33 x + 469 x^{2} - 3531 x^{3} + 11449 x^{4}$ |
Frobenius angles: | $\pm0.0184782107058$, $\pm0.296438695563$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1890117.1 |
Galois group: | $D_{4}$ |
Jacobians: | $8$ |
Isomorphism classes: | 8 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $8355$ | $129360465$ | $1500606985365$ | $17181445456939725$ | $196712138388749156400$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $75$ | $11299$ | $1224945$ | $131076427$ | $14025303600$ | $1500726167791$ | $160578099725475$ | $17181861460952323$ | $1838459211435469125$ | $196715135733376387414$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=40x^6+48x^5+23x^4+52x^3+33x^2+67x+16$
- $y^2=96x^6+71x^5+96x^4+51x^3+48x+26$
- $y^2=97x^6+47x^5+42x^4+82x^3+21x^2+44x+12$
- $y^2=91x^6+99x^5+101x^4+41x^3+2x^2+50x+106$
- $y^2=105x^6+97x^5+100x^4+104x^3+x^2+25x+52$
- $y^2=80x^6+61x^5+31x^4+36x^3+44x^2+99x+69$
- $y^2=91x^6+27x^5+90x^4+89x^3+44x^2+58x+5$
- $y^2=91x^6+106x^5+66x^4+91x^3+22x^2+26x+17$
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 4.0.1890117.1. |
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.bh_sb | $2$ | (not in LMFDB) |