manYPoints - Table of Curves with Many Points http://www.manypoints.org manYPoints aims at providing an open access up-to-date source for information on curves over finite fields with many points Upper bound 2479247 for q=2476099, g=1 http://www.manypoints.org/Details.aspx?e1=3046 Lower bound 2479247 for q=2476099, g=1 http://www.manypoints.org/Details.aspx?e1=3047 Deuring, Max Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Sem. Hansischen Univ. 14, (1941). 197--272. This number of point is reached by the curve y^2=x^3+(1/4)*x^2+a^{508237}*x+a^1608725, where a satisfies the minimal polynomial X^5+5*X+17 in F_19[X]. Upper bound 1422241 for q=1419857, g=1 http://www.manypoints.org/Details.aspx?e1=3044 Lower bound 1422241 for q=1419857, g=1 http://www.manypoints.org/Details.aspx?e1=3045 Deuring, Max Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Sem. Hansischen Univ. 14, (1941). 197--272. This number of point is reached by the curve y^2=x^3+(3/4)*x^2+a^{1351944}*x+a^{198311}, where a satisfies the minimal polynomial X^5+X+14 in F_17[X]. Upper bound 372512 for q=371293, g=1 http://www.manypoints.org/Details.aspx?e1=3042 Lower bound 372512 for q=371293, g=1 http://www.manypoints.org/Details.aspx?e1=3043 Deuring, Max Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Sem. Hansischen Univ. 14, (1941). 197--272. This number of point is reached by the curve y^2=x^3+a*x+a^333760, where a satisfies the minimal polynomial X^5+4*X+11 in F_13[X]. Upper bound 161854 for q=161051, g=1 http://www.manypoints.org/Details.aspx?e1=3040 Lower bound 161854 for q=161051, g=1 http://www.manypoints.org/Details.aspx?e1=3041 Deuring, Max Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Sem. Hansischen Univ. 14, (1941). 197--272. This number of point is reached by the curve y^2=x^3+x+1. Upper bound 3237 for q=3125, g=1 http://www.manypoints.org/Details.aspx?e1=3037 Lower bound 3237 for q=3125, g=1 http://www.manypoints.org/Details.aspx?e1=3038 Deuring, Max Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Sem. Hansischen Univ. 14, (1941). 197--272. This number of point is reached by the curve y^2=x^3+a^97*x+1, where a satisfies Minimal polynomial x^5+4*X+3 in F_5[X]. Upper bound 275 for q=243, g=1 http://www.manypoints.org/Details.aspx?e1=3035 Lower bound 275 for q=243, g=1 http://www.manypoints.org/Details.aspx?e1=3036 Deuring, Max Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Sem. Hansischen Univ. 14, (1941). 197--272. This number of point is reached by the curve y^2=x^3++2*x^2+x+1. Upper bound 131044 for q=130321, g=1 http://www.manypoints.org/Details.aspx?e1=3033 Lower bound 131044 for q=130321, g=1 http://www.manypoints.org/Details.aspx?e1=3034 Deuring, Max Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Sem. Hansischen Univ. 14, (1941). 197--272. This number of point is reached by the curve y^2=x^3+a^2*x, where a satisfies Minimal polynomial x^4+2*X^2+11*X+2 in F_19[X]. Upper bound 84100 for q=83521, g=1 http://www.manypoints.org/Details.aspx?e1=3031 Lower bound 84100 for q=83521, g=1 http://www.manypoints.org/Details.aspx?e1=3032 Deuring, Max Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Sem. Hansischen Univ. 14, (1941). 197--272. This number of point is reached by the curve y^2=x^3+a^3, where a satisfies Minimal polynomial x^4+7*X^2+10*X+3 in F_17[X]. Upper bound 28900 for q=28561, g=1 http://www.manypoints.org/Details.aspx?e1=3029 Lower bound 28900 for q=28561, g=1 http://www.manypoints.org/Details.aspx?e1=3030 Deuring, Max Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Sem. Hansischen Univ. 14, (1941). 197--272. This number of point is reached by the curve y^2=x^3+a^2*x+4*a^3, where a satisfies Minimal polynomial X^4+3*X^2+12*X+2 in F_13[X]. Upper bound 14884 for q=14641, g=1 http://www.manypoints.org/Details.aspx?e1=3027 Lower bound 14884 for q=14641, g=1 http://www.manypoints.org/Details.aspx?e1=3028 Deuring, Max Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Sem. Hansischen Univ. 14, (1941). 197--272. This number of point is reached by the curve y^2=x^3+a^2*x, where a satisfies Minimal polynomial X^4+8*X^2+10*X+2 in F_11[X].