LMFDB - Elliptic curves over $\Q(\sqrt{-3}) $ of conductor 553.2

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Base field	Conductor norm	Rank*	Torsion order	CM discriminant

Base field degree/signature	Bad $p$	$\Q$-curves	Torsion structure	CM

Analytic order of Ш*	Cyclic isogeny degree	Isogeny class size	Reduction	Galois image

j-invariant	Regulator*	Curves per isogeny class	Isogeny class degree	Nonmax$\ \ell$

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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
553.2-a1	553.2-a	$1$	$1$	$\Q(\sqrt{-3}) $	$2$	$[0, 1]$	553.2	$ 7 \cdot 79 $	$ 7 \cdot 79 $	$0.75055$	$(-3a+1), (10a-3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	$ 1 $	$0.032459368$	$8.244746797$	0.618040249	$ \frac{45056}{553} a + \frac{65536}{553} $	$ \bigl[0$ , $ 1$ , $ a + 1$ , $ 0$ , $ -a\bigr] $	${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}-a$

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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.

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