Invariants
Base field: | $\F_{107}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 19 x + 107 x^{2} )( 1 - 16 x + 107 x^{2} )$ |
$1 - 35 x + 518 x^{2} - 3745 x^{3} + 11449 x^{4}$ | |
Frobenius angles: | $\pm0.129482033963$, $\pm0.218559897265$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $8$ |
Isomorphism classes: | 20 |
This isogeny class is not 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $8188$ | $128944624$ | $1501075023856$ | $17184801285635776$ | $196719801719982712468$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $73$ | $11261$ | $1225324$ | $131102025$ | $14025849983$ | $1500733592822$ | $160578169524629$ | $17181861874330129$ | $1838459212077006388$ | $196715135722395359261$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=15x^6+76x^5+14x^4+92x^3+7x^2+35x+32$
- $y^2=24x^6+65x^5+63x^4+45x^3+65x^2+80x+28$
- $y^2=12x^6+33x^5+95x^4+105x^3+100x^2+4x+38$
- $y^2=2x^6+27x^5+29x^4+19x^3+99x^2+49x+93$
- $y^2=51x^6+37x^5+63x^4+6x^3+29x^2+12x+89$
- $y^2=53x^6+43x^5+21x^4+64x^3+61x^2+52x+82$
- $y^2=33x^6+80x^5+7x^4+58x^3+20x^2+33x+106$
- $y^2=9x^6+74x^5+87x^4+14x^3+71x^2+10x+89$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{107}$.
Endomorphism algebra over $\F_{107}$The isogeny class factors as 1.107.at $\times$ 1.107.aq and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.ad_adm | $2$ | (not in LMFDB) |
2.107.d_adm | $2$ | (not in LMFDB) |
2.107.bj_ty | $2$ | (not in LMFDB) |