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Results (4 matches)

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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
36.1-a1 36.1-a \(\Q(\sqrt{6}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $5.898343969$ 1.203994421 \( 0 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 198 a - 485\bigr] \) ${y}^2={x}^{3}+198a-485$
36.1-a2 36.1-a \(\Q(\sqrt{6}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/6\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $17.69503190$ 1.203994421 \( 0 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \) ${y}^2={x}^{3}+1$
36.1-a3 36.1-a \(\Q(\sqrt{6}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $1$ $11.79668793$ 1.203994421 \( 54000 \) \( \bigl[a\) , \( 0\) , \( a\) , \( -6\) , \( -6\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-6{x}-6$
36.1-a4 36.1-a \(\Q(\sqrt{6}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/6\Z$ $-12$ $N(\mathrm{U}(1))$ $1$ $35.39006381$ 1.203994421 \( 54000 \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -75 a - 183\) , \( 507 a + 1242\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-75a-183\right){x}+507a+1242$
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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.