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Download displayed columns for resultsLabel | Class | Base field | Conductor norm | Rank | Torsion | CM | Sato-Tate | Weierstrass equation |
---|---|---|---|---|---|---|---|---|
16.5-a1 | 16.5-a | \(\Q(\sqrt{209}) \) | \( 2^{4} \) | $1$ | $\mathsf{trivial}$ | $-11$ | $N(\mathrm{U}(1))$ | ${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-931337a-6266403\right){x}-1351685915a-9094705362$ |
16.5-a2 | 16.5-a | \(\Q(\sqrt{209}) \) | \( 2^{4} \) | $1$ | $\mathsf{trivial}$ | $-11$ | $N(\mathrm{U}(1))$ | ${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(317a-2430\right){x}-7754a+59890$ |
*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.