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Results (4 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
81.1-a7 81.1-a \(\Q(\sqrt{5}) \) \( 3^{4} \) 0 $\Z/6\Z$ $-60$ $N(\mathrm{U}(1))$ $1$ $23.62521625$ 0.586973216 \( 16554983445 a + 10231546590 \) \( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( 13 \phi - 26\) , \( 32 \phi - 51\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(13\phi-26\right){x}+32\phi-51$
81.1-a8 81.1-a \(\Q(\sqrt{5}) \) \( 3^{4} \) 0 $\Z/2\Z$ $-60$ $N(\mathrm{U}(1))$ $1$ $2.625024027$ 0.586973216 \( 16554983445 a + 10231546590 \) \( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( 114 \phi - 237\) , \( -754 \phi + 1014\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(114\phi-237\right){x}-754\phi+1014$
2025.1-e7 2025.1-e \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) 0 $\Z/2\Z$ $-60$ $N(\mathrm{U}(1))$ $1$ $3.521839301$ 1.575014416 \( 16554983445 a + 10231546590 \) \( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( -6 \phi - 69\) , \( -172 \phi + 55\bigr] \) ${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-6\phi-69\right){x}-172\phi+55$
2025.1-e8 2025.1-e \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) 0 $\Z/2\Z$ $-60$ $N(\mathrm{U}(1))$ $1$ $3.521839301$ 1.575014416 \( 16554983445 a + 10231546590 \) \( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( -59 \phi - 624\) , \( 5383 \phi - 804\bigr] \) ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-59\phi-624\right){x}+5383\phi-804$
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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.