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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-a1 81.1-a \(\Q(\sqrt{5}) \) \( 3^{4} \) 0 $\Z/6\Z$ $-15$ $N(\mathrm{U}(1))$ $1$ $23.62521625$ 0.586973216 \( -85995 a - 52515 \) \( \bigl[1\) , \( -1\) , \( \phi\) , \( -2 \phi\) , \( \phi\bigr] \) ${y}^2+{x}{y}+\phi{y}={x}^{3}-{x}^{2}-2\phi{x}+\phi$
81.1-a2 81.1-a \(\Q(\sqrt{5}) \) \( 3^{4} \) 0 $\Z/2\Z$ $-15$ $N(\mathrm{U}(1))$ $1$ $2.625024027$ 0.586973216 \( -85995 a - 52515 \) \( \bigl[1\) , \( -1\) , \( \phi + 1\) , \( -14 \phi - 2\) , \( -21 \phi - 6\bigr] \) ${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}-{x}^{2}+\left(-14\phi-2\right){x}-21\phi-6$
2025.1-e1 2025.1-e \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) 0 $\Z/2\Z$ $-15$ $N(\mathrm{U}(1))$ $1$ $3.521839301$ 1.575014416 \( -85995 a - 52515 \) \( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( -6 \phi + 6\) , \( -7 \phi + 10\bigr] \) ${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-6\phi+6\right){x}-7\phi+10$
2025.1-e2 2025.1-e \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) 0 $\Z/2\Z$ $-15$ $N(\mathrm{U}(1))$ $1$ $3.521839301$ 1.575014416 \( -85995 a - 52515 \) \( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( -59 \phi + 51\) , \( 253 \phi - 264\bigr] \) ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-59\phi+51\right){x}+253\phi-264$
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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.