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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
51.2-a2 51.2-a \(\Q(\zeta_{9})^+\) \( 3 \cdot 17 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $11.81161603$ 0.656200891 \( \frac{257154008212105}{60886809} a^{2} + \frac{479060149170145}{60886809} a + \frac{139274003304361}{60886809} \) \( \bigl[a^{2} - 1\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 2\) , \( 85 a^{2} - 49 a - 279\) , \( 599 a^{2} - 256 a - 1795\bigr] \) ${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(85a^{2}-49a-279\right){x}+599a^{2}-256a-1795$
153.1-b3 153.1-b \(\Q(\zeta_{9})^+\) \( 3^{2} \cdot 17 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $17.44502313$ 0.969167952 \( \frac{257154008212105}{60886809} a^{2} + \frac{479060149170145}{60886809} a + \frac{139274003304361}{60886809} \) \( \bigl[a\) , \( -a\) , \( a^{2} + a - 1\) , \( -24 a^{2} - 25 a - 61\) , \( a^{2} + 407 a + 289\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}-a{x}^{2}+\left(-24a^{2}-25a-61\right){x}+a^{2}+407a+289$
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  *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.