Invariants
Base field: | $\F_{107}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 37 x + 553 x^{2} - 3959 x^{3} + 11449 x^{4}$ |
Frobenius angles: | $\pm0.0615358508181$, $\pm0.201040771877$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.398333.1 |
Galois group: | $D_{4}$ |
Jacobians: | $7$ |
Isomorphism classes: | 7 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $8007$ | $128103993$ | $1499326371657$ | $17182164941185149$ | $196716570086744379312$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $71$ | $11187$ | $1223897$ | $131081915$ | $14025619576$ | $1500731326791$ | $160578149455627$ | $17181861704462275$ | $1838459210636669297$ | $196715135710865373462$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 7 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=58x^6+33x^5+63x^4+62x^3+93x^2+27x+103$
- $y^2=86x^6+6x^5+59x^4+x^3+88x^2+105x+32$
- $y^2=98x^6+45x^5+18x^4+62x^3+73x^2+26x+45$
- $y^2=18x^6+9x^5+103x^4+52x^3+83x^2+19x+24$
- $y^2=69x^6+25x^5+71x^4+61x^3+65x^2+18x+66$
- $y^2=89x^5+61x^4+93x^3+69x^2+18x+23$
- $y^2=101x^6+55x^5+2x^4+60x^3+3x^2+10x+9$
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 4.0.398333.1. |
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.bl_vh | $2$ | (not in LMFDB) |