Elliptic curves over $\Q$ of conductor 459

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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
459.a1	459b1	459.a	459b	$1$	$1$	\( 3^{3} \cdot 17 \)	\( - 3^{3} \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$0.222162134$	$1$		$6$	$60$	$-0.569439$	$110592/289$	$0.90890$	$2.63771$	$[0, 0, 1, 3, -4]$	\(y^2+y=x^3+3x-4\)	6.2.0.a.1	$[(4, 8)]$
459.b1	459g1	459.b	459g	$1$	$1$	\( 3^{3} \cdot 17 \)	\( - 3^{3} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$102$	$2$	$0$	$1$	$1$		$0$	$66$	$-0.436174$	$-242970624/17$	$1.34713$	$3.68808$	$[0, 0, 1, -39, -94]$	\(y^2+y=x^3-39x-94\)	102.2.0.?	$[]$
459.c1	459h1	459.c	459h	$1$	$1$	\( 3^{3} \cdot 17 \)	\( - 3^{9} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$102$	$2$	$0$	$0.179911424$	$1$		$6$	$36$	$-0.260870$	$-27/17$	$0.99575$	$3.29192$	$[1, -1, 1, -2, 28]$	\(y^2+xy+y=x^3-x^2-2x+28\)	102.2.0.?	$[(-2, 5)]$
459.d1	459f1	459.d	459f	$2$	$3$	\( 3^{3} \cdot 17 \)	\( - 3^{9} \cdot 17 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$102$	$16$	$0$	$1$	$1$		$2$	$54$	$-0.145938$	$-884736/17$	$0.94133$	$3.85267$	$[0, 0, 1, -54, 155]$	\(y^2+y=x^3-54x+155\)	3.8.0-3.a.1.2, 102.16.0.?	$[]$
459.d2	459f2	459.d	459f	$2$	$3$	\( 3^{3} \cdot 17 \)	\( - 3^{11} \cdot 17^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$102$	$16$	$0$	$1$	$1$		$0$	$162$	$0.403368$	$6291456/4913$	$1.15047$	$4.52590$	$[0, 0, 1, 216, 722]$	\(y^2+y=x^3+216x+722\)	3.8.0-3.a.1.1, 102.16.0.?	$[]$
459.e1	459c1	459.e	459c	$2$	$3$	\( 3^{3} \cdot 17 \)	\( - 3^{3} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$102$	$16$	$0$	$1$	$1$		$0$	$18$	$-0.695245$	$-884736/17$	$0.94133$	$2.77719$	$[0, 0, 1, -6, -6]$	\(y^2+y=x^3-6x-6\)	3.8.0-3.a.1.1, 102.16.0.?	$[]$
459.e2	459c2	459.e	459c	$2$	$3$	\( 3^{3} \cdot 17 \)	\( - 3^{5} \cdot 17^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$102$	$16$	$0$	$1$	$1$		$2$	$54$	$-0.145938$	$6291456/4913$	$1.15047$	$3.45041$	$[0, 0, 1, 24, -27]$	\(y^2+y=x^3+24x-27\)	3.8.0-3.a.1.2, 102.16.0.?	$[]$
459.f1	459a1	459.f	459a	$1$	$1$	\( 3^{3} \cdot 17 \)	\( - 3^{3} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$102$	$2$	$0$	$0.898608312$	$1$		$2$	$12$	$-0.810176$	$-27/17$	$0.99575$	$2.21644$	$[1, -1, 0, 0, -1]$	\(y^2+xy=x^3-x^2-1\)	102.2.0.?	$[(2, 1)]$
459.g1	459d1	459.g	459d	$1$	$1$	\( 3^{3} \cdot 17 \)	\( - 3^{9} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$102$	$2$	$0$	$1$	$1$		$0$	$198$	$0.113132$	$-242970624/17$	$1.34713$	$4.76356$	$[0, 0, 1, -351, 2531]$	\(y^2+y=x^3-351x+2531\)	102.2.0.?	$[]$
459.h1	459e1	459.h	459e	$1$	$1$	\( 3^{3} \cdot 17 \)	\( - 3^{9} \cdot 17^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$180$	$-0.020133$	$110592/289$	$0.90890$	$3.71319$	$[0, 0, 1, 27, 101]$	\(y^2+y=x^3+27x+101\)	6.2.0.a.1	$[]$

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