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Download displayed columns for resultsLabel | Class | Base field | Conductor norm | Rank | Torsion | CM | Sato-Tate | Weierstrass equation |
---|---|---|---|---|---|---|---|---|
57.1-f1 | 57.1-f | 4.4.19821.1 | \( 3 \cdot 19 \) | $1$ | $\mathsf{trivial}$ | $\mathrm{SU}(2)$ | ${y}^2+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+2a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{1}{3}a^{2}-6a+3\right){x}^{2}+\left(2a^{3}-5a^{2}-13a+16\right){x}+\frac{4}{3}a^{3}-\frac{14}{3}a^{2}-12a+22$ |
*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.