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Results (4 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
36.1-a4 36.1-a \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{2} \) $0$ $\Z/10\Z$ $1$ $3.855336279$ 1.069277895 \( -\frac{1025795879759761}{3486784401} a + \frac{5304841542920801}{6973568802} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -420 a - 565\) , \( -6327 a - 8227\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-420a-565\right){x}-6327a-8227$
108.1-a4 108.1-a \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{3} \) $0$ $\Z/2\Z$ $1$ $4.010392437$ 1.112282735 \( -\frac{1025795879759761}{3486784401} a + \frac{5304841542920801}{6973568802} \) \( \bigl[a\) , \( a\) , \( a\) , \( 1072 a - 2535\) , \( -26573 a + 61324\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(1072a-2535\right){x}-26573a+61324$
108.2-a4 108.2-a \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{3} \) $0$ $\Z/2\Z$ $1$ $1.002598109$ 1.112282735 \( -\frac{1025795879759761}{3486784401} a + \frac{5304841542920801}{6973568802} \) \( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -689 a - 1001\) , \( -15308 a - 20337\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-689a-1001\right){x}-15308a-20337$
324.1-f4 324.1-f \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{4} \) $0$ $\Z/2\Z$ $1$ $1.042921183$ 1.157017170 \( -\frac{1025795879759761}{3486784401} a + \frac{5304841542920801}{6973568802} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -3770 a - 5085\) , \( 172133 a + 223258\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-3770a-5085\right){x}+172133a+223258$
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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.