Elliptic curves over \(\Q(\sqrt{-2}) \) of conductor 400.1

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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
400.1-a1	400.1-a	$4$	$4$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	400.1	\( 2^{4} \cdot 5^{2} \)	\( 2^{8} \cdot 5^{8} \)	$1.13031$	$(a), (5)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{3} \)	$0.722205338$	$2.996888981$	1.530440152	\( \frac{237276}{625} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( 4\) , \( -6\bigr] \)	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+4{x}-6$
400.1-a2	400.1-a	$4$	$4$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	400.1	\( 2^{4} \cdot 5^{2} \)	\( 2^{4} \cdot 5^{4} \)	$1.13031$	$(a), (5)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2 \)	$1.444410676$	$5.993777963$	1.530440152	\( \frac{148176}{25} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \)	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-{x}$
400.1-a3	400.1-a	$4$	$4$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	400.1	\( 2^{4} \cdot 5^{2} \)	\( 2^{8} \cdot 5^{2} \)	$1.13031$	$(a), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 1 \)	$0.722205338$	$5.993777963$	1.530440152	\( \frac{55296}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \)	${y}^2={x}^{3}-2{x}-1$
400.1-a4	400.1-a	$4$	$4$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	400.1	\( 2^{4} \cdot 5^{2} \)	\( 2^{8} \cdot 5^{2} \)	$1.13031$	$(a), (5)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2 \)	$2.888821352$	$2.996888981$	1.530440152	\( \frac{132304644}{5} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( -26\) , \( -40\bigr] \)	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-26{x}-40$
400.1-b1	400.1-b	$4$	$6$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	400.1	\( 2^{4} \cdot 5^{2} \)	\( 2^{4} \cdot 5^{12} \)	$1.13031$	$(a), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	\( 2 \cdot 3 \)	$1$	$2.141031885$	2.270907247	\( -\frac{20720464}{15625} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( -8\) , \( -17\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-8{x}-17$
400.1-b2	400.1-b	$4$	$6$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	400.1	\( 2^{4} \cdot 5^{2} \)	\( 2^{4} \cdot 5^{4} \)	$1.13031$	$(a), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	\( 2 \)	$1$	$6.423095656$	2.270907247	\( \frac{21296}{25} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( 2\) , \( 1\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+2{x}+1$
400.1-b3	400.1-b	$4$	$6$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	400.1	\( 2^{4} \cdot 5^{2} \)	\( 2^{8} \cdot 5^{2} \)	$1.13031$	$(a), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	\( 2 \)	$1$	$6.423095656$	2.270907247	\( \frac{16384}{5} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \)	${y}^2={x}^{3}-{x}^{2}-{x}$
400.1-b4	400.1-b	$4$	$6$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	400.1	\( 2^{4} \cdot 5^{2} \)	\( 2^{8} \cdot 5^{6} \)	$1.13031$	$(a), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	\( 2 \cdot 3 \)	$1$	$2.141031885$	2.270907247	\( \frac{488095744}{125} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \)	${y}^2={x}^{3}-{x}^{2}-41{x}+116$

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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.