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Results (7 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
361.1-a1 361.1-a \(\Q(\sqrt{5}) \) \( 19^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.205438503$ 0.826874026 \( -\frac{50357871050752}{19} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-769{x}-8470$
361.1-a2 361.1-a \(\Q(\sqrt{5}) \) \( 19^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $1.848946532$ 0.826874026 \( -\frac{89915392}{6859} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-9{x}-15$
361.1-a3 361.1-a \(\Q(\sqrt{5}) \) \( 19^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $16.64051879$ 0.826874026 \( \frac{32768}{19} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+{x}$
361.1-b1 361.1-b \(\Q(\sqrt{5}) \) \( 19^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.29161993$ 1.150638088 \( \frac{27}{19} \) \( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( \phi + 1\) , \( 0\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(\phi+1\right){x}$
361.1-b2 361.1-b \(\Q(\sqrt{5}) \) \( 19^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.145809966$ 1.150638088 \( -\frac{76062245858406}{130321} a + \frac{123071651932059}{130321} \) \( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( \phi - 29\) , \( 38 \phi - 50\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(\phi-29\right){x}+38\phi-50$
361.1-b3 361.1-b \(\Q(\sqrt{5}) \) \( 19^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.29161993$ 1.150638088 \( \frac{13312053}{361} \) \( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -4 \phi - 4\) , \( -12 \phi - 9\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-4\phi-4\right){x}-12\phi-9$
361.1-b4 361.1-b \(\Q(\sqrt{5}) \) \( 19^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.145809966$ 1.150638088 \( \frac{76062245858406}{130321} a + \frac{47009406073653}{130321} \) \( \bigl[\phi\) , \( -\phi - 1\) , \( \phi\) , \( -30\) , \( -38 \phi + 17\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}-30{x}-38\phi+17$
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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.