Invariants
Base field: | $\F_{107}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 33 x + 472 x^{2} - 3531 x^{3} + 11449 x^{4}$ |
Frobenius angles: | $\pm0.0637283762988$, $\pm0.289119628508$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.14633496.1 |
Galois group: | $D_{4}$ |
Jacobians: | $32$ |
Isomorphism classes: | 32 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $8358$ | $129431988$ | $1500971664024$ | $17182418433786144$ | $196713908757529881018$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $75$ | $11305$ | $1225242$ | $131083849$ | $14025429825$ | $1500727819570$ | $160578118103835$ | $17181861661076689$ | $1838459213896036014$ | $196715135767111266025$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 32 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=65x^6+105x^5+6x^3+50x^2+6x+12$
- $y^2=54x^6+54x^5+37x^4+7x^3+13x^2+39x+75$
- $y^2=4x^6+92x^5+78x^4+11x^3+97x^2+48x+42$
- $y^2=81x^6+106x^5+23x^4+75x^3+67x^2+66x+94$
- $y^2=68x^6+93x^5+72x^4+60x^3+85x^2+35x+80$
- $y^2=24x^6+83x^5+94x^4+9x^3+94x^2+47x+58$
- $y^2=17x^6+31x^5+80x^4+81x^3+93x^2+22x+81$
- $y^2=47x^6+82x^5+62x^4+83x^3+93x^2+39x+8$
- $y^2=50x^6+85x^5+64x^4+20x^3+23x^2+78x+99$
- $y^2=73x^6+54x^5+75x^4+98x^3+25x^2+69x+98$
- $y^2=96x^6+79x^5+10x^4+64x^3+74x^2+26x+104$
- $y^2=78x^6+62x^5+89x^4+72x^3+78x^2+79x+3$
- $y^2=95x^6+104x^5+78x^4+11x^3+76x^2+89x+88$
- $y^2=41x^6+54x^5+100x^4+47x^3+68x^2+66x+68$
- $y^2=19x^6+67x^5+38x^4+44x^3+100x^2+9x+23$
- $y^2=75x^6+32x^5+22x^4+74x^3+65x^2+46x+8$
- $y^2=82x^6+26x^5+67x^4+42x^3+6x^2+77x+88$
- $y^2=31x^6+44x^5+4x^4+42x^3+59x^2+3x+99$
- $y^2=70x^6+99x^5+103x^4+24x^3+27x^2+48x+14$
- $y^2=31x^6+51x^5+64x^4+95x^3+49x^2+29x+63$
- and 12 more
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 4.0.14633496.1. |
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_se | $2$ | (not in LMFDB) |