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Download displayed columns for resultsLabel | Class | Base field | Conductor norm | Rank | Torsion | CM | Sato-Tate | Weierstrass equation |
---|---|---|---|---|---|---|---|---|
48.1-b1 | 48.1-b | 4.4.19821.1 | \( 2^{4} \cdot 3 \) | 0 | $\mathsf{trivial}$ | $\mathrm{SU}(2)$ | ${y}^2+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){x}^{2}+\left(-\frac{82}{3}a^{3}+\frac{113}{3}a^{2}+211a-238\right){x}+\frac{478}{3}a^{3}-\frac{626}{3}a^{2}-1188a+1349$ |
*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.