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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
44217.7-a1 44217.7-a \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\Z/2\Z$ $1$ $0.107477719$ 0.303992898 \( -\frac{372082589114986904}{2610969633} a - \frac{181318779827784209}{2610969633} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 2191 a - 26002\) , \( -203191 a + 1594414\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(2191a-26002\right){x}-203191a+1594414$
44217.7-a2 44217.7-a \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.214955439$ 0.303992898 \( \frac{147770521717808}{17596287801} a - \frac{136210703475223}{17596287801} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 151 a - 1607\) , \( -2693 a + 25042\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(151a-1607\right){x}-2693a+25042$
44217.7-a3 44217.7-a \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\Z/2\Z$ $1$ $0.107477719$ 0.303992898 \( \frac{1695948356939509768}{15730800405203547} a - \frac{7330062339265374821}{15730800405203547} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -1889 a - 332\) , \( -61139 a + 75226\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-1889a-332\right){x}-61139a+75226$
44217.7-a4 44217.7-a \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\Z/4\Z$ $1$ $0.429910879$ 0.303992898 \( -\frac{3780522976}{2255067} a + \frac{417620747}{2255067} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 151 a - 162\) , \( 1353 a + 188\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(151a-162\right){x}+1353a+188$
44217.7-b1 44217.7-b \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\Z/4\Z$ $1$ $0.107477719$ 2.735936085 \( \frac{372082589114986904}{2610969633} a - \frac{181318779827784209}{2610969633} \) \( \bigl[1\) , \( 0\) , \( a\) , \( 16 a + 26186\) , \( -1153284 a + 4369\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(16a+26186\right){x}-1153284a+4369$
44217.7-b2 44217.7-b \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.214955439$ 2.735936085 \( -\frac{147770521717808}{17596287801} a - \frac{136210703475223}{17596287801} \) \( \bigl[1\) , \( 0\) , \( a\) , \( 16 a + 1621\) , \( -18381 a - 544\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(16a+1621\right){x}-18381a-544$
44217.7-b3 44217.7-b \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\Z/2\Z$ $1$ $0.107477719$ 2.735936085 \( -\frac{1695948356939509768}{15730800405203547} a - \frac{7330062339265374821}{15730800405203547} \) \( \bigl[1\) , \( 0\) , \( a\) , \( -1904 a + 16\) , \( -63222 a + 70787\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-1904a+16\right){x}-63222a+70787$
44217.7-b4 44217.7-b \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\Z/2\Z$ $1$ $0.429910879$ 2.735936085 \( \frac{3780522976}{2255067} a + \frac{417620747}{2255067} \) \( \bigl[1\) , \( 0\) , \( a\) , \( 136 a + 186\) , \( 60 a - 1825\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(136a+186\right){x}+60a-1825$
44217.7-c1 44217.7-c \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $1$ $\mathsf{trivial}$ $1.281220041$ $0.407318629$ 4.428169593 \( -\frac{23100424192}{14739} \) \( \bigl[0\) , \( -a\) , \( a + 1\) , \( -712 a - 60\) , \( -6669 a + 7446\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-712a-60\right){x}-6669a+7446$
44217.7-c2 44217.7-c \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $1$ $\mathsf{trivial}$ $0.427073347$ $1.221955888$ 4.428169593 \( \frac{32768}{459} \) \( \bigl[0\) , \( -a\) , \( a + 1\) , \( 8 a\) , \( -39 a + 51\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+8a{x}-39a+51$
44217.7-d1 44217.7-d \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\mathsf{trivial}$ $1$ $0.524935341$ 1.484741359 \( \frac{14811123712}{96702579} a + \frac{26737709056}{96702579} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -49 a - 76\) , \( 462 a - 505\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}+\left(-49a-76\right){x}+462a-505$
44217.7-e1 44217.7-e \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $1$ $\mathsf{trivial}$ $1.186590409$ $0.524935341$ 15.85601871 \( -\frac{14811123712}{96702579} a + \frac{26737709056}{96702579} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -55 a + 68\) , \( 429 a - 505\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+\left(-55a+68\right){x}+429a-505$
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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.