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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
169.3-a1 169.3-a \(\Q(\sqrt{3}) \) \( 13^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $3.313232303$ 0.956447781 \( 0 \) \( \bigl[0\) , \( -a\) , \( a\) , \( 1\) , \( 162 a - 280\bigr] \) ${y}^2+a{y}={x}^{3}-a{x}^{2}+{x}+162a-280$
169.3-a2 169.3-a \(\Q(\sqrt{3}) \) \( 13^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $3.313232303$ 0.956447781 \( 0 \) \( \bigl[0\) , \( a\) , \( 1\) , \( 1\) , \( -162 a + 279\bigr] \) ${y}^2+{y}={x}^{3}+a{x}^{2}+{x}-162a+279$
169.3-b1 169.3-b \(\Q(\sqrt{3}) \) \( 13^{2} \) $1$ $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.164334034$ $28.96600420$ 1.374122605 \( 1728 \) \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 8 a - 14\) , \( -7 a + 12\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(8a-14\right){x}-7a+12$
169.3-b2 169.3-b \(\Q(\sqrt{3}) \) \( 13^{2} \) $1$ $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.328668069$ $14.48300210$ 1.374122605 \( 1728 \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -a + 3\) , \( a - 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+3\right){x}+a-1$
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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.