Elliptic curves over \(\Q(\sqrt{-3}) \) of conductor 1648.1

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 150000 over imaginary quadratic fields with absolute discriminant 3

Note: The completeness Only modular elliptic curves are included

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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
1648.1-a1	1648.1-a	$2$	$3$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	1648.1	\( 2^{4} \cdot 103 \)	\( 2^{16} \cdot 103 \)	$0.98614$	$(11a-9), (2)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.1[2]	$1$	\( 3 \)	$1$	$3.415927057$	1.314790937	\( -\frac{263664}{103} a + \frac{948496}{103} \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( -6 a + 1\) , \( 7 a - 6\bigr] \)	${y}^2={x}^{3}-a{x}^{2}+\left(-6a+1\right){x}+7a-6$
1648.1-a2	1648.1-a	$2$	$3$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	1648.1	\( 2^{4} \cdot 103 \)	\( 2^{16} \cdot 103^{3} \)	$0.98614$	$(11a-9), (2)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.1[2]	$1$	\( 3^{2} \)	$1$	$1.138642352$	1.314790937	\( \frac{313125253072}{1092727} a + \frac{408855315152}{1092727} \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( -126 a + 41\) , \( -433 a + 402\bigr] \)	${y}^2={x}^{3}-a{x}^{2}+\left(-126a+41\right){x}-433a+402$

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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.