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Results (16 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
441.1-a1 441.1-a \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $3.014980985$ 1.348340487 \( \frac{300763}{35721} \) \( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( -2 \phi + 3\) , \( 17 \phi - 30\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-2\phi+3\right){x}+17\phi-30$
441.1-a2 441.1-a \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $12.05992394$ 1.348340487 \( \frac{5177717}{189} \) \( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -3 \phi - 3\) , \( -9 \phi - 6\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}+\left(-3\phi-3\right){x}-9\phi-6$
441.1-b1 441.1-b \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 7^{2} \) $0$ $\Z/4\Z$ $1$ $11.04890414$ 1.235305037 \( \frac{2967217}{189} a - \frac{14532341}{567} \) \( \bigl[\phi\) , \( -\phi\) , \( \phi\) , \( -3\) , \( -2 \phi\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}-\phi{x}^{2}-3{x}-2\phi$
441.1-b2 441.1-b \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $11.04890414$ 1.235305037 \( -\frac{5300015616722532145}{7} a + \frac{25726816226286915413}{21} \) \( \bigl[\phi + 1\) , \( \phi - 1\) , \( \phi + 1\) , \( -142 \phi - 199\) , \( -670 \phi + 101\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-142\phi-199\right){x}-670\phi+101$
441.1-b3 441.1-b \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $11.04890414$ 1.235305037 \( -\frac{12214665265}{21} a + \frac{415283030098}{441} \) \( \bigl[\phi\) , \( -\phi\) , \( \phi\) , \( -48\) , \( -101 \phi + 54\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}-\phi{x}^{2}-48{x}-101\phi+54$
441.1-b4 441.1-b \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $2.762226036$ 1.235305037 \( \frac{46991733203041}{343} a + \frac{609892519727245}{7203} \) \( \bigl[1\) , \( -\phi + 1\) , \( \phi\) , \( 98 \phi - 269\) , \( -1112 \phi + 1370\bigr] \) ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(98\phi-269\right){x}-1112\phi+1370$
441.1-c1 441.1-c \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 7^{2} \) $0$ $\Z/4\Z$ $1$ $11.04890414$ 1.235305037 \( -\frac{2967217}{189} a - \frac{5630690}{567} \) \( \bigl[\phi + 1\) , \( -1\) , \( \phi + 1\) , \( -2 \phi - 3\) , \( \phi - 2\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}-{x}^{2}+\left(-2\phi-3\right){x}+\phi-2$
441.1-c2 441.1-c \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $2.762226036$ 1.235305037 \( -\frac{46991733203041}{343} a + \frac{1596718916991106}{7203} \) \( \bigl[1\) , \( \phi\) , \( \phi + 1\) , \( -99 \phi - 171\) , \( 1111 \phi + 258\bigr] \) ${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}+\phi{x}^{2}+\left(-99\phi-171\right){x}+1111\phi+258$
441.1-c3 441.1-c \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $11.04890414$ 1.235305037 \( \frac{12214665265}{21} a + \frac{158775059533}{441} \) \( \bigl[\phi + 1\) , \( -1\) , \( \phi + 1\) , \( -2 \phi - 48\) , \( 100 \phi - 47\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}-{x}^{2}+\left(-2\phi-48\right){x}+100\phi-47$
441.1-c4 441.1-c \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $11.04890414$ 1.235305037 \( \frac{5300015616722532145}{7} a + \frac{9826769376119318978}{21} \) \( \bigl[\phi\) , \( \phi + 1\) , \( 1\) , \( 142 \phi - 339\) , \( 471 \phi - 427\bigr] \) ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(142\phi-339\right){x}+471\phi-427$
441.1-d1 441.1-d \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.814020435$ 0.728082011 \( -\frac{4354703137}{17294403} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) ${y}^2+{x}{y}={x}^{3}-34{x}-217$
441.1-d2 441.1-d \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 7^{2} \) $0$ $\Z/4\Z$ $1$ $13.02432697$ 0.728082011 \( \frac{103823}{63} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}$
441.1-d3 441.1-d \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $13.02432697$ 0.728082011 \( \frac{7189057}{3969} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) ${y}^2+{x}{y}={x}^{3}-4{x}-1$
441.1-d4 441.1-d \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 7^{2} \) $0$ $\Z/8\Z$ $1$ $13.02432697$ 0.728082011 \( \frac{6570725617}{45927} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) ${y}^2+{x}{y}={x}^{3}-39{x}+90$
441.1-d5 441.1-d \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $3.256081743$ 0.728082011 \( \frac{13027640977}{21609} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) ${y}^2+{x}{y}={x}^{3}-49{x}-136$
441.1-d6 441.1-d \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.814020435$ 0.728082011 \( \frac{53297461115137}{147} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) ${y}^2+{x}{y}={x}^{3}-784{x}-8515$
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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.