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Download displayed columns for resultsLabel | Class | Base field | Conductor norm | Rank | Torsion | CM | Sato-Tate | Weierstrass equation |
---|---|---|---|---|---|---|---|---|
36.1-a1 | 36.1-a | \(\Q(\sqrt{53}) \) | \( 2^{2} \cdot 3^{2} \) | 0 | $\mathsf{trivial}$ | $\mathrm{SU}(2)$ | ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a+6\right){x}+4a+11$ | |
324.1-f1 | 324.1-f | \(\Q(\sqrt{53}) \) | \( 2^{2} \cdot 3^{4} \) | $1$ | $\mathsf{trivial}$ | $\mathrm{SU}(2)$ | ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(6a-19\right){x}-8a+43$ |
*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.