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Download displayed columns for resultsLabel | Class | Base field | Conductor norm | Rank | Torsion | CM | Sato-Tate | Weierstrass equation |
---|---|---|---|---|---|---|---|---|
47.1-a1 | 47.1-a | 4.4.19821.1 | \( 47 \) | $1$ | $\mathsf{trivial}$ | $\mathrm{SU}(2)$ | ${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-2\right){x}^{2}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+4a+1\right){x}+\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1$ |
*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.