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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-a5 81.1-a \(\Q(\sqrt{5}) \) \( 3^{4} \) 0 $\Z/6\Z$ $-60$ $N(\mathrm{U}(1))$ $1$ $23.62521625$ 0.586973216 \( -16554983445 a + 26786530035 \) \( \bigl[\phi\) , \( -\phi - 1\) , \( \phi + 1\) , \( -13 \phi - 14\) , \( -20 \phi - 6\bigr] \) ${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-13\phi-14\right){x}-20\phi-6$
81.1-a6 81.1-a \(\Q(\sqrt{5}) \) \( 3^{4} \) 0 $\Z/2\Z$ $-60$ $N(\mathrm{U}(1))$ $1$ $2.625024027$ 0.586973216 \( -16554983445 a + 26786530035 \) \( \bigl[\phi\) , \( -\phi - 1\) , \( \phi\) , \( -113 \phi - 125\) , \( 867 \phi + 384\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-113\phi-125\right){x}+867\phi+384$
2025.1-e5 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 \( -16554983445 a + 26786530035 \) \( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( 6 \phi - 76\) , \( 178 \phi - 193\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(6\phi-76\right){x}+178\phi-193$
2025.1-e6 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 \( -16554983445 a + 26786530035 \) \( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( 59 \phi - 683\) , \( -5324 \phi + 3896\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+{x}^{2}+\left(59\phi-683\right){x}-5324\phi+3896$
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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.