Elliptic curves over $\Q$ of conductor 32

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
32.a1	32a3	32.a	32a	$4$	$4$	\( 2^{5} \)	\( 2^{9} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-16$	$N(\mathrm{U}(1))$		✓	$2$	16.192.3.554	2B				$1$	$1$		$1$	$4$	$-0.617386$	$287496$	$1.17246$	$5.42664$	$[0, 0, 0, -11, -14]$	\(y^2=x^3-11x-14\)		$[]$
32.a2	32a4	32.a	32a	$4$	$4$	\( 2^{5} \)	\( 2^{9} \)	$0$	$\Z/4\Z$	$\Q(\sqrt{-1})$	$-16$	$N(\mathrm{U}(1))$		✓	$2$	16.192.3.540	2B				$1$	$1$		$3$	$4$	$-0.617386$	$287496$	$1.17246$	$5.42664$	$[0, 0, 0, -11, 14]$	\(y^2=x^3-11x+14\)		$[]$
32.a3	32a2	32.a	32a	$4$	$4$	\( 2^{5} \)	\( 2^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓	$2$	16.384.9.568	2Cs				$1$	$1$		$3$	$2$	$-0.963960$	$1728$		$3.35098$	$[0, 0, 0, -1, 0]$	\(y^2=x^3-x\)		$[]$
32.a4	32a1	32.a	32a	$4$	$4$	\( 2^{5} \)	\( - 2^{12} \)	$0$	$\Z/4\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓	$2$	16.384.9.633	2B				$1$	$1$		$3$	$1$	$-0.617386$	$1728$		$4.55098$	$[0, 0, 0, 4, 0]$	\(y^2=x^3+4x\)		$[]$

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