Elliptic curves over \(\Q(\sqrt{-2}) \) of conductor 1458.6

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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
1458.6-a1	1458.6-a	$2$	$3$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	1458.6	\( 2 \cdot 3^{6} \)	\( 2^{2} \cdot 3^{13} \)	$1.56179$	$(a), (-a-1), (a-1)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.1	$1$	\( 2^{2} \cdot 3^{2} \)	$0.098252494$	$3.735412167$	2.076142234	\( -\frac{646679}{1458} a + \frac{382013}{1458} \)	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -a - 3\) , \( 2\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-a-3\right){x}+2$
1458.6-a2	1458.6-a	$2$	$3$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	1458.6	\( 2 \cdot 3^{6} \)	\( 2^{6} \cdot 3^{15} \)	$1.56179$	$(a), (-a-1), (a-1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.2	$1$	\( 2^{2} \)	$0.294757483$	$1.245137389$	2.076142234	\( -\frac{473225423}{72} a + \frac{14377079}{72} \)	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -91 a - 48\) , \( -405 a + 128\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-91a-48\right){x}-405a+128$
1458.6-b1	1458.6-b	$2$	$3$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	1458.6	\( 2 \cdot 3^{6} \)	\( 2^{21} \cdot 3^{6} \)	$1.56179$	$(a), (-a-1), (a-1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.2	$1$	\( 1 \)	$1$	$2.174747898$	1.537778986	\( -\frac{31635919}{6144} a + \frac{1878611}{768} \)	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 2 a - 14\) , \( -8 a + 12\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-14\right){x}-8a+12$
1458.6-b2	1458.6-b	$2$	$3$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	1458.6	\( 2 \cdot 3^{6} \)	\( 2^{7} \cdot 3^{14} \)	$1.56179$	$(a), (-a-1), (a-1)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.1	$1$	\( 3^{2} \)	$1$	$2.174747898$	1.537778986	\( \frac{4823791}{432} a + \frac{1143199}{54} \)	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -4 a - 18\) , \( 12 a + 26\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-4a-18\right){x}+12a+26$

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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.