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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
51.1-a5 51.1-a \(\Q(\zeta_{9})^+\) \( 3 \cdot 17 \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $188.9858566$ 0.656200891 \( \frac{57227017}{153} a^{2} - \frac{97672967}{153} a - \frac{40772771}{153} \) \( \bigl[a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( 0\) , \( -3 a^{2} + 17 a + 7\) , \( 17 a^{2} - 13 a - 7\bigr] \) ${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(-3a^{2}+17a+7\right){x}+17a^{2}-13a-7$
153.3-b6 153.3-b \(\Q(\zeta_{9})^+\) \( 3^{2} \cdot 17 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $17.44502313$ 0.969167952 \( \frac{57227017}{153} a^{2} - \frac{97672967}{153} a - \frac{40772771}{153} \) \( \bigl[a^{2} - 2\) , \( a^{2} - 2\) , \( a + 1\) , \( -3 a^{2} + a + 3\) , \( -3 a^{2} + 1\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-3a^{2}+a+3\right){x}-3a^{2}+1$
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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.