Invariants
Base field: | $\F_{107}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 56 x^{2} + 11449 x^{4}$ |
Frobenius angles: | $\pm0.207861377967$, $\pm0.792138622033$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{30}, \sqrt{-158})\) |
Galois group: | $C_2^2$ |
Jacobians: | $224$ |
Isomorphism classes: | 768 |
This isogeny class is simple but not 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $11394$ | $129823236$ | $1500732099666$ | $17187043241204496$ | $196715135701756650114$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $108$ | $11338$ | $1225044$ | $131119126$ | $14025517308$ | $1500733847482$ | $160578147647844$ | $17181861541564318$ | $1838459212420154508$ | $196715135674556767978$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 224 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=82x^6+62x^5+25x^4+32x^3+38x^2+101x+40$
- $y^2=57x^6+17x^5+50x^4+64x^3+76x^2+95x+80$
- $y^2=61x^6+55x^5+45x^4+57x^3+4x^2+25x+88$
- $y^2=15x^6+3x^5+90x^4+7x^3+8x^2+50x+69$
- $y^2=60x^6+77x^5+23x^4+102x^3+58x^2+27x+81$
- $y^2=13x^6+47x^5+46x^4+97x^3+9x^2+54x+55$
- $y^2=30x^6+13x^5+16x^4+71x^3+23x^2+54x+88$
- $y^2=60x^6+26x^5+32x^4+35x^3+46x^2+x+69$
- $y^2=4x^6+61x^5+102x^4+103x^3+69x^2+91x+68$
- $y^2=8x^6+15x^5+97x^4+99x^3+31x^2+75x+29$
- $y^2=75x^6+82x^5+13x^4+4x^3+22x^2+42x+73$
- $y^2=43x^6+57x^5+26x^4+8x^3+44x^2+84x+39$
- $y^2=79x^6+44x^5+93x^4+91x^3+8x^2+56x+26$
- $y^2=51x^6+88x^5+79x^4+75x^3+16x^2+5x+52$
- $y^2=26x^6+22x^5+42x^4+2x^3+4x^2+31x+24$
- $y^2=52x^6+44x^5+84x^4+4x^3+8x^2+62x+48$
- $y^2=99x^6+101x^5+4x^4+67x^3+10x^2+16x+21$
- $y^2=91x^6+95x^5+8x^4+27x^3+20x^2+32x+42$
- $y^2=16x^6+101x^5+6x^4+65x^3+70x^2+58x+55$
- $y^2=32x^6+95x^5+12x^4+23x^3+33x^2+9x+3$
- and 204 more
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{107^{2}}$.
Endomorphism algebra over $\F_{107}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{30}, \sqrt{-158})\). |
The base change of $A$ to $\F_{107^{2}}$ is 1.11449.ace 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-1185}) \)$)$ |
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.a_ce | $4$ | (not in LMFDB) |