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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
44217.6-a1 44217.6-a \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\Z/2\Z$ $1$ $0.107477719$ 0.303992898 \( \frac{372082589114986904}{2610969633} a - \frac{181318779827784209}{2610969633} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2191 a - 26002\) , \( 203191 a + 1594414\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-2191a-26002\right){x}+203191a+1594414$
44217.6-a2 44217.6-a \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.214955439$ 0.303992898 \( -\frac{147770521717808}{17596287801} a - \frac{136210703475223}{17596287801} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -151 a - 1607\) , \( 2693 a + 25042\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-151a-1607\right){x}+2693a+25042$
44217.6-a3 44217.6-a \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\Z/2\Z$ $1$ $0.107477719$ 0.303992898 \( -\frac{1695948356939509768}{15730800405203547} a - \frac{7330062339265374821}{15730800405203547} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 1889 a - 332\) , \( 61139 a + 75226\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(1889a-332\right){x}+61139a+75226$
44217.6-a4 44217.6-a \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\Z/4\Z$ $1$ $0.429910879$ 0.303992898 \( \frac{3780522976}{2255067} a + \frac{417620747}{2255067} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -151 a - 162\) , \( -1353 a + 188\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-151a-162\right){x}-1353a+188$
44217.6-b1 44217.6-b \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\Z/4\Z$ $1$ $0.107477719$ 2.735936085 \( -\frac{372082589114986904}{2610969633} a - \frac{181318779827784209}{2610969633} \) \( \bigl[1\) , \( 0\) , \( a\) , \( -17 a + 26186\) , \( 1153284 a + 4369\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-17a+26186\right){x}+1153284a+4369$
44217.6-b2 44217.6-b \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.214955439$ 2.735936085 \( \frac{147770521717808}{17596287801} a - \frac{136210703475223}{17596287801} \) \( \bigl[1\) , \( 0\) , \( a\) , \( -17 a + 1621\) , \( 18381 a - 544\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-17a+1621\right){x}+18381a-544$
44217.6-b3 44217.6-b \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\Z/2\Z$ $1$ $0.107477719$ 2.735936085 \( \frac{1695948356939509768}{15730800405203547} a - \frac{7330062339265374821}{15730800405203547} \) \( \bigl[1\) , \( 0\) , \( a\) , \( 1903 a + 16\) , \( 63222 a + 70787\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(1903a+16\right){x}+63222a+70787$
44217.6-b4 44217.6-b \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\Z/2\Z$ $1$ $0.429910879$ 2.735936085 \( -\frac{3780522976}{2255067} a + \frac{417620747}{2255067} \) \( \bigl[1\) , \( 0\) , \( a\) , \( -137 a + 186\) , \( -60 a - 1825\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-137a+186\right){x}-60a-1825$
44217.6-c1 44217.6-c \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $1$ $\mathsf{trivial}$ $1.281220041$ $0.407318629$ 4.428169593 \( -\frac{23100424192}{14739} \) \( \bigl[0\) , \( a\) , \( a + 1\) , \( 712 a - 60\) , \( 6668 a + 7446\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(712a-60\right){x}+6668a+7446$
44217.6-c2 44217.6-c \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $1$ $\mathsf{trivial}$ $0.427073347$ $1.221955888$ 4.428169593 \( \frac{32768}{459} \) \( \bigl[0\) , \( a\) , \( a + 1\) , \( -8 a\) , \( 38 a + 51\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}-8a{x}+38a+51$
44217.6-d1 44217.6-d \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 17^{3} \) $0$ $\mathsf{trivial}$ $1$ $0.524935341$ 1.484741359 \( -\frac{14811123712}{96702579} a + \frac{26737709056}{96702579} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( 49 a - 76\) , \( -462 a - 505\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}+\left(49a-76\right){x}-462a-505$
44217.6-e1 44217.6-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.