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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
529.3-a1 529.3-a \(\Q(\sqrt{-10}) \) \( 23^{2} \) 0 $\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ $1$ $2.646045189$ 0.836752959 \( 8000 \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 3 a - 3\) , \( -3 a + 16\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(3a-3\right){x}-3a+16$
529.3-a2 529.3-a \(\Q(\sqrt{-10}) \) \( 23^{2} \) 0 $\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ $1$ $2.646045189$ 0.836752959 \( 8000 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 10 a - 25\) , \( 33 a + 24\bigr] \) ${y}^2={x}^3-a{x}^2+\left(10a-25\right){x}+33a+24$
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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.