Elliptic curves over \(\Q(\sqrt{-3}) \) of conductor 553.3

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

Results (unique match)

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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
553.3-a1	553.3-a	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	553.3	\( 7 \cdot 79 \)	\( 7 \cdot 79 \)	$0.75055$	$(3a-2), (10a-7)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 1 \)	$0.032459368$	$8.244746797$	0.618040249	\( -\frac{45056}{553} a + \frac{110592}{553} \)	\( \bigl[0\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \)	${y}^2+a{y}={x}^{3}+{x}^{2}$

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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.