Elliptic curves over \(\Q(\sqrt{-447}) \) of conductor 18.2

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 100 over imaginary quadratic fields with absolute discriminant 447

Note: The completeness Only modular elliptic curves are included

Results (displaying both matches)

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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
18.2-a1	18.2-a	$1$	$1$	\(\Q(\sqrt{-447}) \)	$2$	$[0, 1]$	18.2	\( 2 \cdot 3^{2} \)	\( 2^{5} \cdot 3^{9} \cdot 19^{12} \)	$3.89144$	$(2,a+1), (3,a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$5$	5S4	$1$	\( 2 \)	$1.401897495$	$4.041827279$	2.144026930	\( \frac{14271}{32} a + \frac{24279}{2} \)	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -98 a - 876\) , \( 3384 a + 13480\bigr] \)	${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-98a-876\right){x}+3384a+13480$
18.2-b1	18.2-b	$1$	$1$	\(\Q(\sqrt{-447}) \)	$2$	$[0, 1]$	18.2	\( 2 \cdot 3^{2} \)	\( 2^{17} \cdot 3^{9} \)	$3.89144$	$(2,a+1), (3,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$5$	5S4	$1$	\( 2 \cdot 5 \)	$1$	$4.041827279$	3.823437407	\( \frac{14271}{32} a + \frac{24279}{2} \)	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 12 a + 219\) , \( -42 a - 573\bigr] \)	${y}^2+a{x}{y}={x}^3+\left(-a+1\right){x}^2+\left(12a+219\right){x}-42a-573$

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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.