Invariants
Base field: | $\F_{113}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 20 x + 113 x^{2} )^{2}$ |
$1 - 40 x + 626 x^{2} - 4520 x^{3} + 12769 x^{4}$ | |
Frobenius angles: | $\pm0.110150159186$, $\pm0.110150159186$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $5$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $8836$ | $158659216$ | $2078435455684$ | $26582897240805376$ | $339458327210053271236$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $74$ | $12422$ | $1440458$ | $163037886$ | $18424437994$ | $2081954547398$ | $235260594199978$ | $26584442536356478$ | $3004041944914578314$ | $339456739062204502022$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 5 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=71x^6+84x^5+70x^4+30x^3+70x^2+84x+71$
- $y^2=64x^6+60x^5+76x^4+93x^3+81x^2+70x+38$
- $y^2=59x^6+54x^5+72x^4+39x^3+72x^2+54x+59$
- $y^2=17x^6+103x^5+26x^4+84x^3+66x^2+102$
- $y^2=32x^6+90x^4+90x^2+32$
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 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-13}) \)$)$ |
Base change
This is a primitive isogeny class.