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Results (32 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
90.1-a1 90.1-a \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.912862642$ 2.302820115 \( -\frac{103412501}{2160} a - \frac{652894927}{4320} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -18 a - 46\) , \( -56 a - 174\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-18a-46\right){x}-56a-174$
90.1-a2 90.1-a \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.912862642$ 2.302820115 \( \frac{424060922274533}{29160} a + \frac{134099859756653}{2916} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -258 a - 846\) , \( -3960 a - 12654\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-258a-846\right){x}-3960a-12654$
90.1-b1 90.1-b \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.912862642$ 1.381692069 \( \frac{103412501}{2160} a - \frac{652894927}{4320} \) \( \bigl[a + 1\) , \( 1\) , \( a\) , \( 5 a - 12\) , \( 12 a - 34\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(5a-12\right){x}+12a-34$
90.1-b2 90.1-b \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.912862642$ 1.381692069 \( -\frac{424060922274533}{29160} a + \frac{134099859756653}{2916} \) \( \bigl[a + 1\) , \( 1\) , \( a\) , \( 65 a - 212\) , \( 560 a - 1794\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(65a-212\right){x}+560a-1794$
90.1-c1 90.1-c \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.912862642$ 1.381692069 \( -\frac{103412501}{2160} a - \frac{652894927}{4320} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -6 a - 12\) , \( -12 a - 34\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a-12\right){x}-12a-34$
90.1-c2 90.1-c \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.912862642$ 1.381692069 \( \frac{424060922274533}{29160} a + \frac{134099859756653}{2916} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -66 a - 212\) , \( -560 a - 1794\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-66a-212\right){x}-560a-1794$
90.1-d1 90.1-d \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.912862642$ 2.302820115 \( \frac{103412501}{2160} a - \frac{652894927}{4320} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 18 a - 46\) , \( 56 a - 174\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(18a-46\right){x}+56a-174$
90.1-d2 90.1-d \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.912862642$ 2.302820115 \( -\frac{424060922274533}{29160} a + \frac{134099859756653}{2916} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 258 a - 846\) , \( 3960 a - 12654\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(258a-846\right){x}+3960a-12654$
90.1-e1 90.1-e \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.078024702$ 1.776497566 \( -\frac{4451448983765985658895227933}{656100} a + \frac{140767176767424108251921384}{6561} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 50600 a - 181335\) , \( 12006120 a - 39192277\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(50600a-181335\right){x}+12006120a-39192277$
90.1-e2 90.1-e \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.248395236$ 1.776497566 \( -\frac{273359449}{1536000} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -55\) , \( -565\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-55{x}-565$
90.1-e3 90.1-e \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $11.23555713$ 1.776497566 \( \frac{357911}{2160} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 5\) , \( 23\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+5{x}+23$
90.1-e4 90.1-e \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.702222320$ 1.776497566 \( -\frac{15634088809357392517}{2824295364810} a + \frac{4944021583885925864}{282429536481} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 740 a - 1875\) , \( 16212 a - 58945\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(740a-1875\right){x}+16212a-58945$
90.1-e5 90.1-e \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.248395236$ 1.776497566 \( \frac{10316097499609}{5859375000} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -1815\) , \( -6165\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-1815{x}-6165$
90.1-e6 90.1-e \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.808889283$ 1.776497566 \( \frac{35578826569}{5314410} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -275\) , \( -1825\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-275{x}-1825$
90.1-e7 90.1-e \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $11.23555713$ 1.776497566 \( \frac{702595369}{72900} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -75\) , \( 135\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-75{x}+135$
90.1-e8 90.1-e \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.248395236$ 1.776497566 \( \frac{4102915888729}{9000000} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -1335\) , \( -20277\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-1335{x}-20277$
90.1-e9 90.1-e \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.702222320$ 1.776497566 \( \frac{15634088809357392517}{2824295364810} a + \frac{4944021583885925864}{282429536481} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -740 a - 1875\) , \( -16212 a - 58945\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-740a-1875\right){x}-16212a-58945$
90.1-e10 90.1-e \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $11.23555713$ 1.776497566 \( \frac{2656166199049}{33750} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -1155\) , \( 13743\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-1155{x}+13743$
90.1-e11 90.1-e \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.312098809$ 1.776497566 \( \frac{16778985534208729}{81000} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -21335\) , \( -1224277\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-21335{x}-1224277$
90.1-e12 90.1-e \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.078024702$ 1.776497566 \( \frac{4451448983765985658895227933}{656100} a + \frac{140767176767424108251921384}{6561} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -50600 a - 181335\) , \( -12006120 a - 39192277\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-50600a-181335\right){x}-12006120a-39192277$
90.1-f1 90.1-f \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.078024702$ 1.776497566 \( -\frac{4451448983765985658895227933}{656100} a + \frac{140767176767424108251921384}{6561} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 12650 a - 45334\) , \( 1494440 a - 4876368\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(12650a-45334\right){x}+1494440a-4876368$
90.1-f2 90.1-f \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.248395236$ 1.776497566 \( -\frac{273359449}{1536000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-14{x}-64$
90.1-f3 90.1-f \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $11.23555713$ 1.776497566 \( \frac{357911}{2160} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}+2$
90.1-f4 90.1-f \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.702222320$ 1.776497566 \( -\frac{15634088809357392517}{2824295364810} a + \frac{4944021583885925864}{282429536481} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 185 a - 469\) , \( 1934 a - 7134\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(185a-469\right){x}+1934a-7134$
90.1-f5 90.1-f \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.248395236$ 1.776497566 \( \frac{10316097499609}{5859375000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-454{x}-544$
90.1-f6 90.1-f \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z\oplus\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2.808889283$ 1.776497566 \( \frac{35578826569}{5314410} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$
90.1-f7 90.1-f \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z\oplus\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $11.23555713$ 1.776497566 \( \frac{702595369}{72900} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-19{x}+26$
90.1-f8 90.1-f \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.248395236$ 1.776497566 \( \frac{4102915888729}{9000000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-334{x}-2368$
90.1-f9 90.1-f \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.702222320$ 1.776497566 \( \frac{15634088809357392517}{2824295364810} a + \frac{4944021583885925864}{282429536481} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -185 a - 469\) , \( -1934 a - 7134\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-185a-469\right){x}-1934a-7134$
90.1-f10 90.1-f \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $11.23555713$ 1.776497566 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-289{x}+1862$
90.1-f11 90.1-f \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.312098809$ 1.776497566 \( \frac{16778985534208729}{81000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-5334{x}-150368$
90.1-f12 90.1-f \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.078024702$ 1.776497566 \( \frac{4451448983765985658895227933}{656100} a + \frac{140767176767424108251921384}{6561} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -12650 a - 45334\) , \( -1494440 a - 4876368\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-12650a-45334\right){x}-1494440a-4876368$
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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.