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Results (6 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
31.1-a6 31.1-a \(\Q(\sqrt{5}) \) \( 31 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $12.87720992$ 0.359928959 \( \frac{6130703730739448}{31} a + \frac{3788983280553597}{31} \) \( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi\) , \( -18 \phi + 15\) , \( 171 \phi - 265\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-18\phi+15\right){x}+171\phi-265$
775.1-a6 775.1-a \(\Q(\sqrt{5}) \) \( 5^{2} \cdot 31 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.686614230$ 1.508553628 \( \frac{6130703730739448}{31} a + \frac{3788983280553597}{31} \) \( \bigl[\phi\) , \( -\phi\) , \( 0\) , \( -94 \phi - 10\) , \( -792 \phi + 537\bigr] \) ${y}^2+\phi{x}{y}={x}^{3}-\phi{x}^{2}+\left(-94\phi-10\right){x}-792\phi+537$
961.2-c6 961.2-c \(\Q(\sqrt{5}) \) \( 31^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $7.096706804$ $0.430920289$ 1.367630581 \( \frac{6130703730739448}{31} a + \frac{3788983280553597}{31} \) \( \bigl[\phi\) , \( -\phi + 1\) , \( 0\) , \( -497 \phi + 344\) , \( 20816 \phi - 37486\bigr] \) ${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-497\phi+344\right){x}+20816\phi-37486$
2511.1-f6 2511.1-f \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 31 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.257128023$ 1.124409487 \( \frac{6130703730739448}{31} a + \frac{3788983280553597}{31} \) \( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( -151 \phi + 133\) , \( -4927 \phi + 7417\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+{x}^{2}+\left(-151\phi+133\right){x}-4927\phi+7417$
3751.4-b6 3751.4-b \(\Q(\sqrt{5}) \) \( 11^{2} \cdot 31 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.103070773$ 2.729376224 \( \frac{6130703730739448}{31} a + \frac{3788983280553597}{31} \) \( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( -334 \phi - 152\) , \( 2250 \phi + 2607\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\phi{x}^{2}+\left(-334\phi-152\right){x}+2250\phi+2607$
3751.6-a6 3751.6-a \(\Q(\sqrt{5}) \) \( 11^{2} \cdot 31 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.723404901$ 2.588132054 \( \frac{6130703730739448}{31} a + \frac{3788983280553597}{31} \) \( \bigl[1\) , \( -\phi - 1\) , \( 1\) , \( -173 \phi + 97\) , \( 3637 \phi - 6703\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-173\phi+97\right){x}+3637\phi-6703$
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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.