Invariants
Base field: | $\F_{113}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 20 x + 113 x^{2} )( 1 - 16 x + 113 x^{2} )$ |
$1 - 36 x + 546 x^{2} - 4068 x^{3} + 12769 x^{4}$ | |
Frobenius angles: | $\pm0.110150159186$, $\pm0.228810695365$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $36$ |
Isomorphism classes: | 92 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $9212$ | $160473040$ | $2082108851228$ | $26587686780928000$ | $339462031324100340572$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $78$ | $12566$ | $1443006$ | $163067262$ | $18424639038$ | $2081954272214$ | $235260561489486$ | $26584441951774078$ | $3004041938042961198$ | $339456739004455819286$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 36 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=71x^6+98x^5+108x^4+40x^3+27x^2+105x+17$
- $y^2=70x^6+58x^5+20x^4+78x^3+68x^2+110x+89$
- $y^2=104x^6+56x^5+43x^4+95x^3+51x^2+19x+79$
- $y^2=27x^6+105x^5+84x^4+63x^3+73x^2+7x+7$
- $y^2=87x^6+25x^5+54x^4+71x^3+54x^2+25x+87$
- $y^2=42x^6+52x^5+85x^4+101x^3+17x^2+71x+16$
- $y^2=34x^6+88x^5+48x^4+37x^3+5x^2+90x+110$
- $y^2=17x^6+90x^5+76x^4+73x^3+11x^2+33x+52$
- $y^2=62x^6+48x^5+93x^4+29x^3+102x^2+19x+10$
- $y^2=35x^6+103x^5+106x^4+41x^3+77x^2+33x+84$
- $y^2=40x^6+68x^5+24x^4+93x^3+24x^2+68x+40$
- $y^2=97x^6+66x^5+82x^4+106x^3+16x^2+x+5$
- $y^2=75x^6+43x^5+66x^4+51x^3+66x^2+43x+75$
- $y^2=77x^6+21x^5+9x^4+107x^3+41x^2+47x+96$
- $y^2=80x^6+75x^5+100x^4+9x^3+52x^2+70x+78$
- $y^2=84x^6+61x^5+9x^4+19x^3+17x^2+85x+66$
- $y^2=49x^6+96x^5+68x^4+63x^3+84x^2+107x+98$
- $y^2=17x^6+15x^5+54x^4+8x^3+54x^2+15x+17$
- $y^2=70x^6+90x^5+99x^4+83x^3+99x^2+90x+70$
- $y^2=88x^6+110x^5+66x^4+81x^3+9x^2+28x+3$
- and 16 more
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{113}$.
Endomorphism algebra over $\F_{113}$The isogeny class factors as 1.113.au $\times$ 1.113.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.