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Results (24 matches)

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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
36300.1-a1 36300.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.229933812$ $0.418120005$ 3.552410420 \( \frac{179310732119}{1392187500} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( 118 a - 119\) , \( 1658\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(118a-119\right){x}+1658$
36300.1-a2 36300.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) $2$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.229933812$ $1.672480023$ 3.552410420 \( \frac{1263214441}{211200} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -22 a + 21\) , \( -22\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-22a+21\right){x}-22$
36300.1-a3 36300.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.229933812$ $0.836240011$ 3.552410420 \( \frac{119168121961}{10890000} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -102 a + 101\) , \( 426\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-102a+101\right){x}+426$
36300.1-a4 36300.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) $2$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.919735251$ $0.418120005$ 3.552410420 \( \frac{455129268177961}{4392300} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -1602 a + 1601\) , \( 25626\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-1602a+1601\right){x}+25626$
36300.1-b1 36300.1-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.118130243$ 2.182480898 \( \frac{116149984977671}{2779502343750} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( 1017 a - 1018\) , \( -79830\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(1017a-1018\right){x}-79830$
36300.1-b2 36300.1-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.118130243$ 2.182480898 \( \frac{7981893677157049}{1917731420550} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -4163 a + 4162\) , \( 81506\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-4163a+4162\right){x}+81506$
36300.1-b3 36300.1-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.236260487$ 2.182480898 \( \frac{312341975961049}{17862322500} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -1413 a + 1412\) , \( -18594\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-1413a+1412\right){x}-18594$
36300.1-b4 36300.1-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.472520975$ 2.182480898 \( \frac{299270638153369}{1069200} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -1393 a + 1392\) , \( -19210\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-1393a+1392\right){x}-19210$
36300.1-c1 36300.1-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.053744214$ 1.985871164 \( -\frac{15595206456730321}{310672490129100} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -5204 a + 5204\) , \( -857220\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-5204a+5204\right){x}-857220$
36300.1-c2 36300.1-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.429953719$ 1.985871164 \( \frac{1833318007919}{1070530560} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 256 a - 256\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(256a-256\right){x}$
36300.1-c3 36300.1-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.214976859$ 1.985871164 \( \frac{119102750067601}{68309049600} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -1024 a + 1024\) , \( 1792\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-1024a+1024\right){x}+1792$
36300.1-c4 36300.1-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.107488429$ 1.985871164 \( \frac{135670761487282321}{643043610000} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -10704 a + 10704\) , \( -418320\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-10704a+10704\right){x}-418320$
36300.1-c5 36300.1-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.107488429$ 1.985871164 \( \frac{182864522286982801}{463015182960} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -11824 a + 11824\) , \( 500752\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-11824a+11824\right){x}+500752$
36300.1-c6 36300.1-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.053744214$ 1.985871164 \( \frac{553808571467029327441}{12529687500} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -171084 a + 171084\) , \( -27137628\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-171084a+171084\right){x}-27137628$
36300.1-d1 36300.1-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.010975077$ 2.838735725 \( \frac{2371297246710590562911}{4084000833203280000} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 277815 a - 277815\) , \( -79390431\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(277815a-277815\right){x}-79390431$
36300.1-d2 36300.1-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.021950154$ 2.838735725 \( \frac{201738262891771037089}{45727545600000000} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -122185 a + 122185\) , \( -12750431\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-122185a+122185\right){x}-12750431$
36300.1-d3 36300.1-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.043900308$ 2.838735725 \( \frac{7220044159551112609}{448454983680000} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -40265 a + 40265\) , \( 2961825\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-40265a+40265\right){x}+2961825$
36300.1-d4 36300.1-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.010975077$ 2.838735725 \( \frac{680995599504466943307169}{52207031250000000} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -1832905 a + 1832905\) , \( -953988575\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-1832905a+1832905\right){x}-953988575$
36300.1-e1 36300.1-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.477210181$ $1.972426006$ 4.347501901 \( \frac{13651919}{126720} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -5 a\) , \( 17\bigr] \) ${y}^2+a{x}{y}={x}^{3}-5a{x}+17$
36300.1-e2 36300.1-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.238605090$ $0.246553250$ 4.347501901 \( \frac{13411719834479}{32153832150} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -495 a\) , \( -7473\bigr] \) ${y}^2+a{x}{y}={x}^{3}-495a{x}-7473$
36300.1-e3 36300.1-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.477210181$ $0.493106501$ 4.347501901 \( \frac{1834216913521}{329422500} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 255 a\) , \( -1323\bigr] \) ${y}^2+a{x}{y}={x}^{3}+255a{x}-1323$
36300.1-e4 36300.1-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.954420362$ $0.986213003$ 4.347501901 \( \frac{46694890801}{3920400} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 75 a\) , \( 225\bigr] \) ${y}^2+a{x}{y}={x}^{3}+75a{x}+225$
36300.1-e5 36300.1-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.954420362$ $0.246553250$ 4.347501901 \( \frac{6484907238722641}{283593750} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 3885 a\) , \( -93525\bigr] \) ${y}^2+a{x}{y}={x}^{3}+3885a{x}-93525$
36300.1-e6 36300.1-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 11^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.908840725$ $0.493106501$ 4.347501901 \( \frac{179415687049201}{1443420} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 1175 a\) , \( 15405\bigr] \) ${y}^2+a{x}{y}={x}^{3}+1175a{x}+15405$
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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.