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Results (20 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
4900.1-a1 4900.1-a \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $4.394590828$ 1.965320765 \( \frac{1367631}{2800} \) \( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( 12 \phi + 12\) , \( 55 \phi + 41\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(12\phi+12\right){x}+55\phi+41$
4900.1-a2 4900.1-a \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $4.394590828$ 1.965320765 \( \frac{611960049}{122500} \) \( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( -88 \phi - 88\) , \( 375 \phi + 281\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-88\phi-88\right){x}+375\phi+281$
4900.1-a3 4900.1-a \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $1.098647707$ 1.965320765 \( \frac{74565301329}{5468750} \) \( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( -438 \phi - 438\) , \( -6345 \phi - 4759\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-438\phi-438\right){x}-6345\phi-4759$
4900.1-a4 4900.1-a \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $4.394590828$ 1.965320765 \( \frac{2121328796049}{120050} \) \( \bigl[\phi\) , \( -\phi - 1\) , \( \phi + 1\) , \( 1338 \phi - 2677\) , \( -33714 \phi + 59332\bigr] \) ${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(1338\phi-2677\right){x}-33714\phi+59332$
4900.1-b1 4900.1-b \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\mathsf{trivial}$ $1$ $2.211195222$ 1.977753131 \( -\frac{417267265}{235298} \) \( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -227 \phi - 227\) , \( 3019 \phi + 2321\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}+\left(-227\phi-227\right){x}+3019\phi+2321$
4900.1-b2 4900.1-b \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\mathsf{trivial}$ $1$ $2.211195222$ 1.977753131 \( \frac{397535}{392} \) \( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( -23 \phi + 45\) , \( 76 \phi - 128\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-23\phi+45\right){x}+76\phi-128$
4900.1-c1 4900.1-c \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $1$ $\mathsf{trivial}$ $0.012846808$ $3.685488049$ 2.794983082 \( -\frac{1026590625}{100352} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -180\) , \( 1047\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-180{x}+1047$
4900.1-d1 4900.1-d \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $3.142886610$ 1.405541621 \( -\frac{548347731625}{1835008} \) \( \bigl[\phi\) , \( -1\) , \( 1\) , \( 852 \phi - 1705\) , \( -17475 \phi + 30581\bigr] \) ${y}^2+\phi{x}{y}+{y}={x}^{3}-{x}^{2}+\left(852\phi-1705\right){x}-17475\phi+30581$
4900.1-d2 4900.1-d \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $3.142886610$ 1.405541621 \( -\frac{15625}{28} \) \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -3 \phi - 3\) , \( -5 \phi - 4\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-3\phi-3\right){x}-5\phi-4$
4900.1-d3 4900.1-d \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $3.142886610$ 1.405541621 \( \frac{9938375}{21952} \) \( \bigl[\phi\) , \( -1\) , \( 1\) , \( -23 \phi + 45\) , \( -115 \phi + 201\bigr] \) ${y}^2+\phi{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-23\phi+45\right){x}-115\phi+201$
4900.1-d4 4900.1-d \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $3.142886610$ 1.405541621 \( \frac{4956477625}{941192} \) \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -178 \phi - 178\) , \( 1395 \phi + 1046\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-178\phi-178\right){x}+1395\phi+1046$
4900.1-d5 4900.1-d \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $3.142886610$ 1.405541621 \( \frac{128787625}{98} \) \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -53 \phi - 53\) , \( -245 \phi - 184\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-53\phi-53\right){x}-245\phi-184$
4900.1-d6 4900.1-d \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $3.142886610$ 1.405541621 \( \frac{2251439055699625}{25088} \) \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -13653 \phi - 13653\) , \( 1102915 \phi + 827186\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-13653\phi-13653\right){x}+1102915\phi+827186$
4900.1-e1 4900.1-e \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\mathsf{trivial}$ $1$ $1.489837150$ 1.332550857 \( \frac{7336753}{6272} a - \frac{1493917}{3136} \) \( \bigl[\phi + 1\) , \( 0\) , \( \phi + 1\) , \( 33 \phi - 5\) , \( 76 \phi - 30\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(33\phi-5\right){x}+76\phi-30$
4900.1-f1 4900.1-f \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\mathsf{trivial}$ $1$ $1.489837150$ 1.332550857 \( -\frac{7336753}{6272} a + \frac{4348919}{6272} \) \( \bigl[\phi\) , \( -\phi + 1\) , \( \phi\) , \( -35 \phi + 30\) , \( -77 \phi + 47\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-35\phi+30\right){x}-77\phi+47$
4900.1-g1 4900.1-g \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $1$ $\mathsf{trivial}$ $0.031126488$ $7.093471642$ 2.764788988 \( \frac{7336753}{6272} a - \frac{1493917}{3136} \) \( \bigl[1\) , \( \phi - 1\) , \( \phi\) , \( 7 \phi - 8\) , \( -16 \phi + 25\bigr] \) ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(7\phi-8\right){x}-16\phi+25$
4900.1-h1 4900.1-h \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $1$ $\mathsf{trivial}$ $0.031126488$ $7.093471642$ 2.764788988 \( -\frac{7336753}{6272} a + \frac{4348919}{6272} \) \( \bigl[1\) , \( -\phi\) , \( \phi + 1\) , \( -8 \phi - 1\) , \( 15 \phi + 9\bigr] \) ${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}-\phi{x}^{2}+\left(-8\phi-1\right){x}+15\phi+9$
4900.1-i1 4900.1-i \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\mathsf{trivial}$ $1$ $0.940068646$ 0.840822958 \( -\frac{1026590625}{100352} \) \( \bigl[\phi\) , \( -\phi - 1\) , \( \phi\) , \( 36 \phi - 72\) , \( 160 \phi - 272\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(36\phi-72\right){x}+160\phi-272$
4900.1-j1 4900.1-j \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $1$ $\mathsf{trivial}$ $0.653095700$ $0.802120939$ 2.811337089 \( -\frac{417267265}{235298} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -45\) , \( -185\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-45{x}-185$
4900.1-j2 4900.1-j \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $1$ $\Z/3\Z$ $0.217698566$ $7.219088453$ 2.811337089 \( \frac{397535}{392} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 5\) , \( 5\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+5{x}+5$
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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.