初 等 整 数 論 講 義 第 $2$ 版

$\blacktriangleleft$ $2.$ 指数表  $4.$ 虚二次体 $\blacktriangleright$

『初等整数論講義 第 $2$ 版』目次へ



数     表

$3.$ 実  二  次  体

 $100$ 以内の $m$ に関して $K\left(\sqrt{m}\right)$ の基本単数 $\varepsilon$ およびイデヤルの類(広義)の数 $h$ の表を掲げる.$d$ は判別式,$N\left(\varepsilon\right)$ の欄に ― を記すのは $N\left(\varepsilon\right)=-1$ を示す.その他は $N\left(\varepsilon\right)=+1$.イデヤルの欄には主類以外の類を代表するものを掲げる.
  $m$    $d$       $\varepsilon$     $\hphantom{1}N\left(\varepsilon\right)\hphantom{1}$ $h$    イ デ ヤ ル   
$\hphantom{1}2$$\hphantom{1}2^3$$\hphantom{1}1+\sqrt{2}$ ― $\hphantom{111}1\hphantom{11}$
$\hphantom{1}3$$\hphantom{1}2^2\hspace{0.7mm}\cdotp3$$\hphantom{1}2+\sqrt{3}$$\hphantom{111}1\hphantom{11}$
$\hphantom{1}5$$\hphantom{1}5$$\hphantom{1}\dfrac{1+\sqrt{5}}{2}$ ― $\hphantom{111}1\hphantom{11}$
$\hphantom{1}6$$\hphantom{1}2^3\hspace{0.7mm}\cdotp3$$\hphantom{1}5+2\sqrt{6}$$\hphantom{111}1\hphantom{11}$
$\hphantom{1}7$$\hphantom{1}2^2\hspace{0.7mm}\cdotp7$$\hphantom{1}8+3\sqrt{7}$$\hphantom{111}1\hphantom{11}$
$10$$\hphantom{1}2^3\hspace{0.7mm}\cdotp5$$\hphantom{1}3+\sqrt{10}$ ― $\hphantom{111}2\hphantom{11}$ $\left[2,\ \sqrt{10}\right]$
$11$$\hphantom{1}2^2\hspace{0.7mm}\cdotp11$$\hphantom{1}10+3\sqrt{11}$$\hphantom{111}1\hphantom{11}$
$13$$\hphantom{1}13$$\hphantom{1}\dfrac{3+\sqrt{13}}{2}$ ― $\hphantom{111}1\hphantom{11}$
$14$$\hphantom{1}2^3\hspace{0.7mm}\cdotp7$$\hphantom{1}15+4\sqrt{14}$$\hphantom{111}1\hphantom{11}$
$15$$\hphantom{1}2^2\hspace{0.7mm}\cdotp3\hspace{0.7mm}\cdotp5$$\hphantom{1}4+\sqrt{15}$$\hphantom{111}2\hphantom{11}$ $\left[2,\ 1+\sqrt{15}\right]$
$17$$\hphantom{1}17$$\hphantom{1}4+\sqrt{17}$ ― $\hphantom{111}1\hphantom{11}$
$19$$\hphantom{1}2^2\hspace{0.7mm}\cdotp19$$\hphantom{1}170+39\sqrt{19}$$\hphantom{111}1\hphantom{11}$
$21$$\hphantom{1}3\hspace{0.7mm}\cdotp7$$\hphantom{1}\dfrac{5+\sqrt{21}}{2}$$\hphantom{111}1\hphantom{11}$
$22$$\hphantom{1}2^3\hspace{0.7mm}\cdotp11$$\hphantom{1}197+42\sqrt{22}$$\hphantom{111}1\hphantom{11}$
$23$$\hphantom{1}2^2\hspace{0.7mm}\cdotp23$$\hphantom{1}24+5\sqrt{23}$$\hphantom{111}1\hphantom{11}$
$26$$\hphantom{1}2^3\hspace{0.7mm}\cdotp13$$\hphantom{1}5+\sqrt{26}$ ― $\hphantom{111}2\hphantom{11}$ $\left[2,\ \sqrt{26}\right]$
$29$$\hphantom{1}29$$\hphantom{1}\dfrac{5+\sqrt{29}}{2}$ ― $\hphantom{111}1\hphantom{11}$
$30$$\hphantom{1}2^3\hspace{0.7mm}\cdotp3\hspace{0.7mm}\cdotp5$$\hphantom{1}11+2\sqrt{30}$$\hphantom{111}2\hphantom{11}$ $\left[2,\ \sqrt{30}\right]$
$31$$\hphantom{1}2^2\hspace{0.7mm}\cdotp31$$\hphantom{1}1520+273\sqrt{31}$$\hphantom{111}1\hphantom{11}$
$33$$\hphantom{1}3\hspace{0.7mm}\cdotp11$$\hphantom{1}23+4\sqrt{33}$$\hphantom{111}1\hphantom{11}$
$34$$\hphantom{1}2^3\hspace{0.7mm}\cdotp17$$\hphantom{1}35+6\sqrt{34}$$\hphantom{111}2\hphantom{11}$ $\left[3,\ 1+\sqrt{34}\right]$
$35$$\hphantom{1}2^2\hspace{0.7mm}\cdotp5\hspace{0.7mm}\cdotp7$$\hphantom{1}6+\sqrt{35}$$\hphantom{111}2\hphantom{11}$ $\left[2,\ 1+\sqrt{35}\right]$

  $m$    $d$       $\varepsilon$     $\hphantom{1}N\left(\varepsilon\right)\hphantom{1}$ $h$    イ デ ヤ ル   
$37$$\hphantom{1}37$$\hphantom{1}6+\sqrt{37}$ ― $\hphantom{111}1\hphantom{11}$
$38$$\hphantom{1}2^3\hspace{0.7mm}\cdotp19$$\hphantom{1}37+6\sqrt{38}$$\hphantom{111}1\hphantom{11}$
$39$$\hphantom{1}2^2\hspace{0.7mm}\cdotp3\hspace{0.7mm}\cdotp13$$\hphantom{1}25+4\sqrt{39}$$\hphantom{111}2\hphantom{11}$ $\left[2,\ 1+\sqrt{39}\right]$
$41$$\hphantom{1}41$$\hphantom{1}32+5\sqrt{41}$ ― $\hphantom{111}1\hphantom{11}$
$42$$\hphantom{1}2^3\hspace{0.7mm}\cdotp3\hspace{0.7mm}\cdotp7$$\hphantom{1}13+2\sqrt{42}$$\hphantom{111}2\hphantom{11}$ $\left[2,\ \sqrt{42}\right]$
$43$$\hphantom{1}2^2\hspace{0.7mm}\cdotp43$$\hphantom{1}3482+531\sqrt{43}$$\hphantom{111}1\hphantom{11}$
$46$$\hphantom{1}2^3\hspace{0.7mm}\cdotp23$$\hphantom{1}24335+3588\sqrt{46}$$\hphantom{111}1\hphantom{11}$
$47$$\hphantom{1}2^2\hspace{0.7mm}\cdotp47$$\hphantom{1}48+7\sqrt{47}$$\hphantom{111}1\hphantom{11}$
$51$$\hphantom{1}2^2\hspace{0.7mm}\cdotp3\hspace{0.7mm}\cdotp17$$\hphantom{1}50+7\sqrt{51}$$\hphantom{111}2\hphantom{11}$ $\left[3,\ \sqrt{51}\right]$
$53$$\hphantom{1}53$$\hphantom{1}\dfrac{7+\sqrt{53}}{2}$ ― $\hphantom{111}1\hphantom{11}$
$55$$\hphantom{1}2^2\hspace{0.7mm}\cdotp5\hspace{0.7mm}\cdotp11$$\hphantom{1}89+12\sqrt{55}$$\hphantom{111}2\hphantom{11}$ $\left[2,\ 1+\sqrt{55}\right]$
$57$$\hphantom{1}3\hspace{0.7mm}\cdotp19$$\hphantom{1}151+20\sqrt{57}$$\hphantom{111}1\hphantom{11}$
$58$$\hphantom{1}2^3\hspace{0.7mm}\cdotp29$$\hphantom{1}99+13\sqrt{58}$ ― $\hphantom{111}2\hphantom{11}$ $\left[2,\ \sqrt{58}\right]$
$59$$\hphantom{1}2^2\hspace{0.7mm}\cdotp59$$\hphantom{1}530+69\sqrt{59}$$\hphantom{111}1\hphantom{11}$
$61$$\hphantom{1}61$$\hphantom{1}\dfrac{39+5\sqrt{61}}{2}$ ― $\hphantom{111}1\hphantom{11}$
$62$$\hphantom{1}2^3\hspace{0.7mm}\cdotp31$$\hphantom{1}63+8\sqrt{62}$$\hphantom{111}1\hphantom{11}$
$65$$\hphantom{1}5\hspace{0.7mm}\cdotp13$$\hphantom{1}8+\sqrt{65}$ ― $\hphantom{111}2\hphantom{11}$ $\left[5,\ \sqrt{65}\right]$
$66$$\hphantom{1}2^3\hspace{0.7mm}\cdotp3\hspace{0.7mm}\cdotp11$$\hphantom{1}65+8\sqrt{66}$$\hphantom{111}2\hphantom{11}$ $\left[3,\ \sqrt{66}\right]$
$67$$\hphantom{1}2^2\hspace{0.7mm}\cdotp67$$\hphantom{1}48842+5967\sqrt{67}$$\hphantom{111}1\hphantom{11}$
$69$$\hphantom{1}3\hspace{0.7mm}\cdotp23$$\hphantom{1}\dfrac{25+3\sqrt{69}}{2}$$\hphantom{111}1\hphantom{11}$
$70$$\hphantom{1}2^3\hspace{0.7mm}\cdotp5\hspace{0.7mm}\cdotp7$$\hphantom{1}251+30\sqrt{70}$$\hphantom{111}2\hphantom{11}$ $\left[2,\ \sqrt{70}\right]$
$71$$\hphantom{1}2^2\hspace{0.7mm}\cdotp71$$\hphantom{1}3480+413\sqrt{71}$$\hphantom{111}1\hphantom{11}$
$73$$\hphantom{1}73$$\hphantom{1}1068+125\sqrt{73}$ ― $\hphantom{111}1\hphantom{11}$
$74$$\hphantom{1}2^3\hspace{0.7mm}\cdotp37$$\hphantom{1}43+5\sqrt{74}$ ― $\hphantom{111}2\hphantom{11}$ $\left[2,\ \sqrt{74}\right]$
$77$$\hphantom{1}7\hspace{0.7mm}\cdotp11$$\hphantom{1}\dfrac{9+\sqrt{77}}{2}$$\hphantom{111}1\hphantom{11}$
$78$$\hphantom{1}2^3\hspace{0.7mm}\cdotp3\hspace{0.7mm}\cdotp13$$\hphantom{1}53+6\sqrt{78}$$\hphantom{111}2\hphantom{11}$ $\left[2,\ \sqrt{78}\right]$
$79$$\hphantom{1}2^2\hspace{0.7mm}\cdotp79$$\hphantom{1}80+9\sqrt{79}$$\hphantom{111}3\hphantom{11}$ $\left[3,\ \pm1+\sqrt{79}\right]$

  $m$    $d$       $\varepsilon$     $\hphantom{1}N\left(\varepsilon\right)\hphantom{1}$ $h$    イ デ ヤ ル   
$82$$\hphantom{1}2^3\hspace{0.7mm}\cdotp41$$\hphantom{1}9+\sqrt{82}$ ― $\hphantom{111}4\hphantom{11}$ $\left[3,\ \pm1+\sqrt{82}\right],\left[2,\ \sqrt{82}\right]$
$83$$\hphantom{1}2^2\hspace{0.7mm}\cdotp83$$\hphantom{1}82+9\sqrt{83}$$\hphantom{111}1\hphantom{11}$
$85$$\hphantom{1}5\hspace{0.7mm}\cdotp17$$\hphantom{1}\dfrac{9+\sqrt{85}}{2}$ ― $\hphantom{111}2\hphantom{11}$ $\left[5,\ \sqrt{85}\right]$
$86$$\hphantom{1}2^3\hspace{0.7mm}\cdotp43$$\hphantom{1}10405+1122\sqrt{86}$$\hphantom{111}1\hphantom{11}$
$87$$\hphantom{1}2^2\hspace{0.7mm}\cdotp3\hspace{0.7mm}\cdotp29$$\hphantom{1}28+3\sqrt{87}$$\hphantom{111}2\hphantom{11}$ $\left[2,\ 1+\sqrt{87}\right]$
$89$$\hphantom{1}89$$\hphantom{1}500+53\sqrt{89}$ ― $\hphantom{111}1\hphantom{11}$
$91$$\hphantom{1}2^2\hspace{0.7mm}\cdotp7\hspace{0.7mm}\cdotp13$$\hphantom{1}1574+165\sqrt{91}$$\hphantom{111}2\hphantom{11}$ $\left[2,\ 1+\sqrt{91}\right]$
$93$$\hphantom{1}3\hspace{0.7mm}\cdotp31$$\hphantom{1}\dfrac{29+3\sqrt{93}}{2}$$\hphantom{111}1\hphantom{11}$
$94$$\hphantom{1}2^3\hspace{0.7mm}\cdotp47$$\hphantom{1}2143295+221064\sqrt{94}$$\hphantom{111}1\hphantom{11}$
$95$$\hphantom{1}2^2\hspace{0.7mm}\cdotp5\hspace{0.7mm}\cdotp19$$\hphantom{1}39+4\sqrt{95}$$\hphantom{111}2\hphantom{11}$ $\left[2,\ 1+\sqrt{95}\right]$
$97$$\hphantom{1}97$$\hphantom{1}5604+569\sqrt{97}$ ― $\hphantom{111}1\hphantom{11}$






$\blacktriangleleft$ $2.$ 指数表  $4.$ 虚二次体 $\blacktriangleright$

『初等整数論講義 第 $2$ 版』目次へ


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