Invariants
Base field: | $\F_{107}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 20 x + 107 x^{2} )( 1 - 14 x + 107 x^{2} )$ |
$1 - 34 x + 494 x^{2} - 3638 x^{3} + 11449 x^{4}$ | |
Frobenius angles: | $\pm0.0823304377774$, $\pm0.263402699857$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $20$ |
Isomorphism classes: | 80 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $8272$ | $129175552$ | $1500938294416$ | $17183287418159104$ | $196716031782848094352$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $74$ | $11282$ | $1225214$ | $131090478$ | $14025581194$ | $1500729693122$ | $160578131311966$ | $17181861676208926$ | $1838459213210445578$ | $196715135764260757682$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=106x^6+39x^5+12x^4+51x^3+39x^2+4x+71$
- $y^2=65x^6+64x^5+83x^4+96x^3+101x^2+50x+58$
- $y^2=77x^6+32x^5+95x^4+26x^3+71x^2+76x+82$
- $y^2=32x^6+81x^4+53x^3+47x^2+96x+94$
- $y^2=38x^6+13x^5+73x^4+83x^3+92x^2+26x+94$
- $y^2=51x^6+3x^5+82x^4+28x^3+82x^2+3x+51$
- $y^2=100x^6+17x^5+31x^4+51x^3+21x^2+48x+57$
- $y^2=34x^6+102x^5+20x^4+34x^3+78x^2+47x+29$
- $y^2=24x^6+91x^5+67x^4+81x^3+29x^2+80x+10$
- $y^2=16x^6+35x^5+73x^4+6x^3+78x^2+18x+95$
- $y^2=36x^6+30x^5+64x^4+74x^3+52x^2+82x+105$
- $y^2=94x^6+88x^5+76x^4+52x^3+76x^2+88x+94$
- $y^2=48x^6+8x^5+62x^4+61x^3+48x^2+6x+94$
- $y^2=96x^6+62x^5+44x^4+51x^3+99x^2+60x+22$
- $y^2=71x^6+76x^5+40x^4+83x^3+72x^2+72x+70$
- $y^2=91x^6+22x^5+4x^4+39x^3+79x^2+67x+97$
- $y^2=20x^6+51x^5+86x^4+85x^3+32x^2+97x$
- $y^2=78x^6+62x^5+82x^4+30x^3+37x^2+6x+102$
- $y^2=94x^6+80x^5+32x^4+80x^3+45x^2+41x+86$
- $y^2=105x^6+42x^5+81x^4+60x^3+41x^2+25x+75$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{107}$.
Endomorphism algebra over $\F_{107}$The isogeny class factors as 1.107.au $\times$ 1.107.ao 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.ag_aco | $2$ | (not in LMFDB) |
2.107.g_aco | $2$ | (not in LMFDB) |
2.107.bi_ta | $2$ | (not in LMFDB) |