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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 \(\Q(\sqrt{3}) \) \( 3^{4} \) 0 $\mathsf{trivial}$ $-27$ $N(\mathrm{U}(1))$ $1$ $1.040337491$ 0.900958696 \( -12288000 \) \( \bigl[0\) , \( 0\) , \( a\) , \( -30\) , \( -64\bigr] \) ${y}^2+a{y}={x}^{3}-30{x}-64$
81.1-a2 81.1-a \(\Q(\sqrt{3}) \) \( 3^{4} \) 0 $\Z/3\Z$ $-27$ $N(\mathrm{U}(1))$ $1$ $28.08911226$ 0.900958696 \( -12288000 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( -30\) , \( 63\bigr] \) ${y}^2+{y}={x}^{3}-30{x}+63$
81.1-a3 81.1-a \(\Q(\sqrt{3}) \) \( 3^{4} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $28.08911226$ 0.900958696 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}$
81.1-a4 81.1-a \(\Q(\sqrt{3}) \) \( 3^{4} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $9.363037422$ 0.900958696 \( 0 \) \( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -1\bigr] \) ${y}^2+a{y}={x}^{3}-1$
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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.