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Download displayed columns for resultsLabel | Class | Base field | Conductor norm | Rank | Torsion | CM | Sato-Tate | Weierstrass equation |
---|---|---|---|---|---|---|---|---|
53.2-a1 | 53.2-a | 5.5.24217.1 | \( 53 \) | $1$ | $\mathsf{trivial}$ | $\mathrm{SU}(2)$ | ${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+1\right){x}{y}+\left(a^{4}-4a^{2}+1\right){y}={x}^{3}+\left(2a^{4}-a^{3}-10a^{2}+3a+4\right){x}^{2}+\left(3a^{4}-3a^{3}-14a^{2}+8a+5\right){x}-3a^{4}+2a^{3}+13a^{2}-7a-4$ |
*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.