Elliptic curves over \(\Q(\sqrt{-2}) \) of conductor 16384.1

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
16384.1-a1	16384.1-a	$2$	$2$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	16384.1	\( 2^{14} \)	\( 2^{21} \)	$2.85949$	$(a)$	$2$	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓			✓			$1$	\( 2 \)	$1.012804378$	$4.088009945$	5.855345308	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a\) , \( 0\bigr] \)	${y}^2={x}^{3}+2a{x}$
16384.1-a2	16384.1-a	$2$	$2$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	16384.1	\( 2^{14} \)	\( 2^{21} \)	$2.85949$	$(a)$	$2$	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓			✓			$1$	\( 2 \)	$1.012804378$	$4.088009945$	5.855345308	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a\) , \( 0\bigr] \)	${y}^2={x}^{3}-2a{x}$
16384.1-b1	16384.1-b	$2$	$2$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	16384.1	\( 2^{14} \)	\( 2^{15} \)	$2.85949$	$(a)$	0	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓			✓			$1$	\( 2 \)	$1$	$5.781319108$	2.044004972	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -a\) , \( 0\bigr] \)	${y}^2={x}^{3}-a{x}$
16384.1-b2	16384.1-b	$2$	$2$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	16384.1	\( 2^{14} \)	\( 2^{15} \)	$2.85949$	$(a)$	0	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓			✓			$1$	\( 2 \)	$1$	$5.781319108$	2.044004972	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( a\) , \( 0\bigr] \)	${y}^2={x}^{3}+a{x}$

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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.