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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 4.4.19821.1 \( 47 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.302657994$ $581.3716021$ 4.999230649 \( -\frac{21742}{47} a^{3} + \frac{8397}{47} a^{2} + \frac{186762}{47} a + \frac{41657}{47} \) \( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 2\) , \( 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 4 a + 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\bigr] \) ${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-2\right){x}^{2}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+4a+1\right){x}+\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1$
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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.