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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
539.1-a3 539.1-a \(\Q(\sqrt{33}) \) \( 7^{2} \cdot 11 \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $0.602881548$ 1.679171307 \( \frac{9463555063808}{115539436859} \) \( \bigl[0\) , \( -a\) , \( 1\) , \( -162165 a + 546870\) , \( -270199791 a + 911189707\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-162165a+546870\right){x}-270199791a+911189707$
539.1-f3 539.1-f \(\Q(\sqrt{33}) \) \( 7^{2} \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $6.706046397$ $0.266569154$ 2.489484723 \( \frac{9463555063808}{115539436859} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+441{x}-15815$
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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.