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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
47.1-a1 47.1-a \(\Q(\sqrt{-11}) \) \( 47 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.037922542$ $7.280811841$ 0.665994884 \( -\frac{598016}{2209} a + \frac{430080}{2209} \) \( \bigl[0\) , \( a\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}+a{x}^{2}-{x}$
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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.