"타원곡선"의 두 판 사이의 차이

2009년 10월 13일 (화) 09:23 판

\(y^2=4x^3-g_2(\tau)x-g_3\)

\(g_2(\tau) = 60G_4=60\sum_{ (m,n) \neq (0,0)} \frac{1}{(m+n\tau )^{4}}\)

\(g_3(\tau) = 140G_6=140\sum_{ (m,n) \neq (0,0)} \frac{1}{(m+n\tau )^{6}}\)

the only possible torsion groups for elliptic curves over Q are the cyclic groups of order 1,2,3,4,5,6,7,8,9,10,12 [sic -- 11 is not possible] and (Z/2)*(Z/2n) for n=1,2,3,4

\(E(\mathbb Q)=\frac{\mathbb Z}{2\mathbb Z}\o \frac{\mathbb Z}{2\mathbb Z}\)

[/pages/2061314/attachments/2299029 MSP1975197gdf732cih44i50000361d01gd578fhc4a.gif]

\(2\omega=4\int_0^1\frac{dx}{\sqrt{1-x^4}}=B(1/2,1/4)=\frac{\Gamma(\frac{1}{2})\Gamma(\frac{1}{4})}{\Gamma(\frac{3}{4})}=5.24\cdots\)

@@ 38번째 줄: / 38번째 줄: @@
 <h5>예</h5>
-<math>y^2=x^3-x</math>
+* <math>y^2=x^3-x</math>
+<math>E(\mathbb Q)=\frac{\mathbb Z}{2\mathbb Z}\o \frac{\mathbb Z}{2\mathbb Z}</math>
 [/pages/2061314/attachments/2299029 MSP1975197gdf732cih44i50000361d01gd578fhc4a.gif]
-<math>y^2=4x^3-4x</math>
 <math>2\omega=4\int_0^1\frac{dx}{\sqrt{1-x^4}}=B(1/2,1/4)=\frac{\Gamma(\frac{1}{2})\Gamma(\frac{1}{4})}{\Gamma(\frac{3}{4})}=5.24\cdots</math>
@@ 80번째 줄: / 90번째 줄: @@
 * [[아이젠슈타인 급수(Eisenstein series)]]<br>
 * [[오일러 베타적분(베타함수)|베타적분]]<br>
-* [[사각 피라미드 퍼즐]]<br>  <br>
+* [[사각 피라미드 퍼즐]]<br>
+* [[congruent number 문제]]<br>
 <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">수학용어번역</h5>