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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
51.3-a3 51.3-a \(\Q(\zeta_{9})^+\) \( 3 \cdot 17 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $11.81161603$ 0.656200891 \( \frac{479060149170145}{60886809} a^{2} - \frac{736214157382250}{60886809} a - \frac{304538278611719}{60886809} \) \( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 2\) , \( -48 a^{2} - 38 a - 12\) , \( -255 a^{2} - 344 a - 86\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-48a^{2}-38a-12\right){x}-255a^{2}-344a-86$
153.2-b4 153.2-b \(\Q(\zeta_{9})^+\) \( 3^{2} \cdot 17 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $17.44502313$ 0.969167952 \( \frac{479060149170145}{60886809} a^{2} - \frac{736214157382250}{60886809} a - \frac{304538278611719}{60886809} \) \( \bigl[a^{2} + a - 2\) , \( -a^{2} + 1\) , \( a^{2} - 1\) , \( -24 a^{2} + 46 a - 61\) , \( 408 a^{2} - 410 a - 524\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(-24a^{2}+46a-61\right){x}+408a^{2}-410a-524$
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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.