Elliptic curves over $\Q$ of conductor 637

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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
637.a1	637d1	637.a	637d	$1$	$1$	\( 7^{2} \cdot 13 \)	\( - 7^{7} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$182$	$2$	$0$	$0.513244526$	$1$		$4$	$192$	$0.036626$	$110592/91$	$0.71571$	$3.60692$	$[0, 0, 1, 49, -86]$	\(y^2+y=x^3+49x-86\)	182.2.0.?	$[(7, 24)]$	$1$
637.b1	637b3	637.b	637b	$3$	$9$	\( 7^{2} \cdot 13 \)	\( - 7^{15} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$1638$	$144$	$3$	$1$	$1$		$0$	$1728$	$1.333059$	$-178643795968/524596891$	$1.15023$	$6.10029$	$[0, -1, 1, -5749, 415463]$	\(y^2+y=x^3-x^2-5749x+415463\)	3.4.0.a.1, 9.12.0.a.1, 21.8.0-3.a.1.2, 63.24.0-9.a.1.2, 78.8.0.?, $\ldots$	$[ ]$	$1$
637.b2	637b1	637.b	637b	$3$	$9$	\( 7^{2} \cdot 13 \)	\( - 7^{7} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$1638$	$144$	$3$	$1$	$1$		$0$	$192$	$0.234447$	$-43614208/91$	$0.87141$	$4.53322$	$[0, -1, 1, -359, -2507]$	\(y^2+y=x^3-x^2-359x-2507\)	3.4.0.a.1, 9.12.0.a.1, 21.8.0-3.a.1.1, 63.24.0-9.a.1.1, 78.8.0.?, $\ldots$	$[ ]$	$1$
637.b3	637b2	637.b	637b	$3$	$9$	\( 7^{2} \cdot 13 \)	\( - 7^{9} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$1638$	$144$	$3$	$1$	$1$		$0$	$576$	$0.783752$	$224755712/753571$	$0.95798$	$5.02934$	$[0, -1, 1, 621, -13238]$	\(y^2+y=x^3-x^2+621x-13238\)	3.12.0.a.1, 21.24.0-3.a.1.1, 78.24.0.?, 117.36.0.?, 182.2.0.?, $\ldots$	$[ ]$	$1$
637.c1	637a1	637.c	637a	$2$	$7$	\( 7^{2} \cdot 13 \)	\( - 7^{4} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.48.0.3	7B.1.2	$364$	$96$	$2$	$0.685355679$	$1$		$2$	$60$	$-0.146044$	$-56723625/13$	$1.28311$	$3.97068$	$[1, -1, 0, -107, 454]$	\(y^2+xy=x^3-x^2-107x+454\)	7.48.0-7.b.1.2, 52.2.0.a.1, 364.96.2.?	$[(6, -2)]$	$1$
637.c2	637a2	637.c	637a	$2$	$7$	\( 7^{2} \cdot 13 \)	\( - 7^{4} \cdot 13^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.48.0.6	7B.1.5	$364$	$96$	$2$	$4.797489755$	$1$		$2$	$420$	$0.826911$	$11397810375/62748517$	$1.05408$	$5.12361$	$[1, -1, 0, 628, -17823]$	\(y^2+xy=x^3-x^2+628x-17823\)	7.48.0-7.b.1.1, 52.2.0.a.1, 364.96.2.?	$[(104, 1027)]$	$1$
637.d1	637c1	637.d	637c	$2$	$7$	\( 7^{2} \cdot 13 \)	\( - 7^{10} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.48.0.6	7B.1.5	$364$	$96$	$2$	$8.826746643$	$1$		$0$	$420$	$0.826911$	$-56723625/13$	$1.28311$	$5.77893$	$[1, -1, 0, -5252, -145223]$	\(y^2+xy=x^3-x^2-5252x-145223\)	7.48.0-7.b.1.1, 52.2.0.a.1, 364.96.2.?	$[(4776/7, 158761/7)]$	$1$
637.d2	637c2	637.d	637c	$2$	$7$	\( 7^{2} \cdot 13 \)	\( - 7^{10} \cdot 13^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.48.0.3	7B.1.2	$364$	$96$	$2$	$1.260963806$	$1$		$2$	$2940$	$1.799866$	$11397810375/62748517$	$1.05408$	$6.93186$	$[1, -1, 0, 30763, 6051758]$	\(y^2+xy=x^3-x^2+30763x+6051758\)	7.48.0-7.b.1.2, 52.2.0.a.1, 364.96.2.?	$[(-38, 2216)]$	$1$

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