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Results (14 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
1083.1-a1 1083.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 19^{2} \) $1$ $\mathsf{trivial}$ $0.037574592$ $30.86363048$ 1.339092757 \( -\frac{1404928}{171} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -2\) , \( 2\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-2{x}+2$
1083.1-b1 1083.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 19^{2} \) $1$ $\Z/4\Z$ $2.601893913$ $2.262154252$ 1.699108754 \( \frac{67419143}{390963} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 7\) , \( -30\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+7{x}-30$
1083.1-b2 1083.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 19^{2} \) $1$ $\Z/4\Z$ $0.650473478$ $36.19446804$ 1.699108754 \( \frac{389017}{57} \) \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 86 a - 146\) , \( -500 a + 867\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(86a-146\right){x}-500a+867$
1083.1-b3 1083.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 19^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.300946956$ $9.048617011$ 1.699108754 \( \frac{30664297}{3249} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -8\) , \( -6\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-8{x}-6$
1083.1-b4 1083.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 19^{2} \) $1$ $\Z/2\Z$ $2.601893913$ $2.262154252$ 1.699108754 \( \frac{115714886617}{1539} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -103\) , \( -386\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-103{x}-386$
1083.1-c1 1083.1-c \(\Q(\sqrt{3}) \) \( 3 \cdot 19^{2} \) $0$ $\mathsf{trivial}$ $1$ $0.085998375$ 0.496511851 \( -\frac{9358714467168256}{22284891} \) \( \bigl[0\) , \( -a + 1\) , \( a\) , \( 245858 a - 425861\) , \( 87559214 a - 151657044\bigr] \) ${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(245858a-425861\right){x}+87559214a-151657044$
1083.1-c2 1083.1-c \(\Q(\sqrt{3}) \) \( 3 \cdot 19^{2} \) $0$ $\Z/5\Z$ $1$ $2.149959381$ 0.496511851 \( \frac{841232384}{1121931} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 20\) , \( -32\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+20{x}-32$
1083.1-d1 1083.1-d \(\Q(\sqrt{3}) \) \( 3 \cdot 19^{2} \) $1$ $\mathsf{trivial}$ $0.226284916$ $3.435258684$ 4.488016288 \( -\frac{9358714467168256}{22284891} \) \( \bigl[0\) , \( a - 1\) , \( 1\) , \( 245858 a - 425861\) , \( -87559214 a + 151657043\bigr] \) ${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(245858a-425861\right){x}-87559214a+151657043$
1083.1-d2 1083.1-d \(\Q(\sqrt{3}) \) \( 3 \cdot 19^{2} \) $1$ $\mathsf{trivial}$ $1.131424581$ $3.435258684$ 4.488016288 \( \frac{841232384}{1121931} \) \( \bigl[0\) , \( -1\) , \( a\) , \( 20\) , \( 31\bigr] \) ${y}^2+a{y}={x}^{3}-{x}^{2}+20{x}+31$
1083.1-e1 1083.1-e \(\Q(\sqrt{3}) \) \( 3 \cdot 19^{2} \) $0$ $\Z/4\Z$ $1$ $4.711524088$ 2.720199700 \( \frac{67419143}{390963} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 8\) , \( 29\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+8{x}+29$
1083.1-e2 1083.1-e \(\Q(\sqrt{3}) \) \( 3 \cdot 19^{2} \) $0$ $\Z/2\Z$ $1$ $18.84609635$ 2.720199700 \( \frac{389017}{57} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 84 a - 147\) , \( 585 a - 1014\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(84a-147\right){x}+585a-1014$
1083.1-e3 1083.1-e \(\Q(\sqrt{3}) \) \( 3 \cdot 19^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $18.84609635$ 2.720199700 \( \frac{30664297}{3249} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -7\) , \( 5\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-7{x}+5$
1083.1-e4 1083.1-e \(\Q(\sqrt{3}) \) \( 3 \cdot 19^{2} \) $0$ $\Z/4\Z$ $1$ $18.84609635$ 2.720199700 \( \frac{115714886617}{1539} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -102\) , \( 385\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-102{x}+385$
1083.1-f1 1083.1-f \(\Q(\sqrt{3}) \) \( 3 \cdot 19^{2} \) $0$ $\mathsf{trivial}$ $1$ $3.679988085$ 4.249284223 \( -\frac{1404928}{171} \) \( \bigl[0\) , \( 1\) , \( a\) , \( -2\) , \( -3\bigr] \) ${y}^2+a{y}={x}^{3}+{x}^{2}-2{x}-3$
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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.