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Results (18 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
20808.5-a1 20808.5-a \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $1.638672685$ 1.158716568 \( -\frac{216259784}{70227} a - \frac{740698438}{70227} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 16 a + 15\) , \( 59\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(16a+15\right){x}+59$
20808.5-a2 20808.5-a \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $0.819336342$ 1.158716568 \( -\frac{6773137523}{17065161} a - \frac{14265581908}{17065161} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -14 a + 55\) , \( 142 a + 187\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-14a+55\right){x}+142a+187$
20808.5-b1 20808.5-b \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $0$ $\mathsf{trivial}$ $1$ $0.595188230$ 0.841723267 \( \frac{57530252288}{38336139} \) \( \bigl[0\) , \( -1\) , \( a\) , \( 128\) , \( 174\bigr] \) ${y}^2+a{y}={x}^{3}-{x}^{2}+128{x}+174$
20808.5-c1 20808.5-c \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $1.638672685$ 1.158716568 \( \frac{216259784}{70227} a - \frac{740698438}{70227} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -16 a + 15\) , \( 59\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-16a+15\right){x}+59$
20808.5-c2 20808.5-c \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $0.819336342$ 1.158716568 \( \frac{6773137523}{17065161} a - \frac{14265581908}{17065161} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 14 a + 55\) , \( -142 a + 187\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(14a+55\right){x}-142a+187$
20808.5-d1 20808.5-d \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $1$ $\mathsf{trivial}$ $0.066462902$ $0.401746248$ 4.908959850 \( -\frac{13596667005814784}{2263710671811} a + \frac{35649488015527936}{2263710671811} \) \( \bigl[0\) , \( a\) , \( a\) , \( -103 a + 468\) , \( -2360 a - 1770\bigr] \) ${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(-103a+468\right){x}-2360a-1770$
20808.5-e1 20808.5-e \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $1$ $\mathsf{trivial}$ $0.066462902$ $0.401746248$ 4.908959850 \( \frac{13596667005814784}{2263710671811} a + \frac{35649488015527936}{2263710671811} \) \( \bigl[0\) , \( -a\) , \( a\) , \( 103 a + 468\) , \( 2360 a - 1770\bigr] \) ${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(103a+468\right){x}+2360a-1770$
20808.5-f1 20808.5-f \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.418645842$ $1.473245113$ 6.977932709 \( -\frac{31250}{23409} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -2\) , \( 42\bigr] \) ${y}^2+a{x}{y}={x}^{3}-2{x}+42$
20808.5-f2 20808.5-f \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z$ $0.837291685$ $0.736622556$ 6.977932709 \( -\frac{5476739736875}{547981281} a + \frac{23093460929000}{547981281} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -110 a + 78\) , \( -40 a + 850\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-110a+78\right){x}-40a+850$
20808.5-f3 20808.5-f \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z$ $0.837291685$ $0.736622556$ 6.977932709 \( \frac{5476739736875}{547981281} a + \frac{23093460929000}{547981281} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 110 a + 78\) , \( 40 a + 850\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(110a+78\right){x}+40a+850$
20808.5-f4 20808.5-f \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z$ $0.837291685$ $2.946490226$ 6.977932709 \( \frac{12194500}{153} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -12\) , \( 18\bigr] \) ${y}^2+a{x}{y}={x}^{3}-12{x}+18$
20808.5-g1 20808.5-g \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $1$ $\mathsf{trivial}$ $0.035837594$ $2.721420930$ 6.896354363 \( -\frac{2249728}{4131} \) \( \bigl[0\) , \( 1\) , \( a\) , \( -4\) , \( -8\bigr] \) ${y}^2+a{y}={x}^{3}+{x}^{2}-4{x}-8$
20808.5-h1 20808.5-h \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.809400023$ 4.578657960 \( \frac{1285471294}{751689} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 72\) , \( -36\bigr] \) ${y}^2+a{x}{y}={x}^{3}+72{x}-36$
20808.5-h2 20808.5-h \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $1.618800046$ 4.578657960 \( \frac{40873252}{23409} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -18\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}-18{x}$
20808.5-h3 20808.5-h \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/4\Z$ $1$ $0.809400023$ 4.578657960 \( \frac{22994537186}{111537} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -188\) , \( 1020\bigr] \) ${y}^2+a{x}{y}={x}^{3}-188{x}+1020$
20808.5-h4 20808.5-h \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $0.404700011$ 4.578657960 \( -\frac{1400716334131201}{20927272323} a + \frac{1883759902489320}{6975757441} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -30 a + 792\) , \( -6036 a - 828\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-30a+792\right){x}-6036a-828$
20808.5-h5 20808.5-h \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $0.404700011$ 4.578657960 \( \frac{1400716334131201}{20927272323} a + \frac{1883759902489320}{6975757441} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 30 a + 792\) , \( 6036 a - 828\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(30a+792\right){x}+6036a-828$
20808.5-h6 20808.5-h \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/4\Z$ $1$ $3.237600092$ 4.578657960 \( \frac{61918288}{153} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -13\) , \( -16\bigr] \) ${y}^2+a{x}{y}={x}^{3}-13{x}-16$
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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.