Elliptic curves over $\Q$ of conductor 209344

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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	Manin constant
209344.a1	209344a1	209344.a	209344a	$1$	$1$	\( 2^{6} \cdot 3271 \)	\( - 2^{10} \cdot 3271 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6542$	$2$	$0$	$14.79250377$	$1$		$0$	$56832$	$0.140576$	$-1674035968/3271$	$0.72210$	$2.29954$	$[0, 1, 0, -249, -1601]$	\(y^2=x^3+x^2-249x-1601\)	6542.2.0.?	$[(2515765/122, 3984044481/122)]$	$1$
209344.b1	209344c1	209344.b	209344c	$1$	$1$	\( 2^{6} \cdot 3271 \)	\( - 2^{10} \cdot 3271 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6542$	$2$	$0$	$7.536351446$	$1$		$2$	$21504$	$-0.068889$	$6912/3271$	$0.65889$	$1.83466$	$[0, 0, 0, 4, 88]$	\(y^2=x^3+4x+88\)	6542.2.0.?	$[(-3, 7), (33/2, 209/2)]$	$1$
209344.c1	209344b1	209344.c	209344b	$1$	$1$	\( 2^{6} \cdot 3271 \)	\( - 2^{10} \cdot 3271 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6542$	$2$	$0$	$1$	$4$	$2$	$0$	$21504$	$-0.068889$	$6912/3271$	$0.65889$	$1.83466$	$[0, 0, 0, 4, -88]$	\(y^2=x^3+4x-88\)	6542.2.0.?	$[ ]$	$1$
209344.d1	209344d1	209344.d	209344d	$1$	$1$	\( 2^{6} \cdot 3271 \)	\( - 2^{10} \cdot 3271 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6542$	$2$	$0$	$4.729856598$	$1$		$0$	$56832$	$0.140576$	$-1674035968/3271$	$0.72210$	$2.29954$	$[0, -1, 0, -249, 1601]$	\(y^2=x^3-x^2-249x+1601\)	6542.2.0.?	$[(185/4, 741/4)]$	$1$

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