Elliptic curves over $\Q$ of conductor 6171

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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
6171.a1	6171e1	6171.a	6171e	$1$	$1$	\( 3 \cdot 11^{2} \cdot 17 \)	\( - 3^{17} \cdot 11^{2} \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$0.267650579$	$1$		$6$	$15504$	$1.135851$	$-87367919423488/37321507107$	$1.00339$	$4.29095$	$[0, 1, 1, -4572, -158416]$	\(y^2+y=x^3+x^2-4572x-158416\)	6.2.0.a.1	$[(342, 6196)]$	$1$
6171.b1	6171c2	6171.b	6171c	$2$	$2$	\( 3 \cdot 11^{2} \cdot 17 \)	\( 3^{10} \cdot 11^{3} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$0.781451798$	$1$		$6$	$2880$	$0.568176$	$97018944875/1003833$	$1.03263$	$3.72288$	$[1, 0, 0, -1053, -13122]$	\(y^2+xy=x^3-1053x-13122\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[(-18, 0)]$	$1$
6171.b2	6171c1	6171.b	6171c	$2$	$2$	\( 3 \cdot 11^{2} \cdot 17 \)	\( 3^{5} \cdot 11^{3} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$0.390725899$	$1$		$7$	$1440$	$0.221603$	$136590875/70227$	$1.04418$	$2.97059$	$[1, 0, 0, -118, 155]$	\(y^2+xy=x^3-118x+155\)	2.3.0.a.1, 66.6.0.a.1, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[(-7, 29)]$	$1$
6171.c1	6171a1	6171.c	6171a	$1$	$1$	\( 3 \cdot 11^{2} \cdot 17 \)	\( - 3^{10} \cdot 11^{7} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$374$	$2$	$0$	$0.536083600$	$1$		$4$	$38400$	$1.804234$	$-5736108018368512/11042163$	$1.03559$	$5.80605$	$[0, -1, 1, -451249, 116824311]$	\(y^2+y=x^3-x^2-451249x+116824311\)	374.2.0.?	$[(763, 14701)]$	$1$
6171.d1	6171f1	6171.d	6171f	$1$	$1$	\( 3 \cdot 11^{2} \cdot 17 \)	\( - 3^{2} \cdot 11^{11} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$374$	$2$	$0$	$1$	$1$		$0$	$19200$	$1.431110$	$-2160697802752/24640803$	$1.02074$	$4.90493$	$[0, 1, 1, -32589, -2297509]$	\(y^2+y=x^3+x^2-32589x-2297509\)	374.2.0.?	$[ ]$	$1$
6171.e1	6171g2	6171.e	6171g	$2$	$3$	\( 3 \cdot 11^{2} \cdot 17 \)	\( - 3 \cdot 11^{6} \cdot 17^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1122$	$16$	$0$	$1$	$1$		$0$	$8100$	$0.939724$	$-23100424192/14739$	$1.03897$	$4.38282$	$[0, 1, 1, -7179, 231875]$	\(y^2+y=x^3+x^2-7179x+231875\)	3.4.0.a.1, 33.8.0-3.a.1.1, 102.8.0.?, 1122.16.0.?	$[ ]$	$1$
6171.e2	6171g1	6171.e	6171g	$2$	$3$	\( 3 \cdot 11^{2} \cdot 17 \)	\( - 3^{3} \cdot 11^{6} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1122$	$16$	$0$	$1$	$1$		$0$	$2700$	$0.390418$	$32768/459$	$1.01165$	$3.20007$	$[0, 1, 1, 81, 1370]$	\(y^2+y=x^3+x^2+81x+1370\)	3.4.0.a.1, 33.8.0-3.a.1.2, 102.8.0.?, 1122.16.0.?	$[ ]$	$1$
6171.f1	6171b2	6171.f	6171b	$2$	$2$	\( 3 \cdot 11^{2} \cdot 17 \)	\( 3^{10} \cdot 11^{9} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$1$		$0$	$31680$	$1.767124$	$97018944875/1003833$	$1.03263$	$5.37137$	$[1, 0, 1, -127416, 17337967]$	\(y^2+xy+y=x^3-127416x+17337967\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[ ]$	$1$
6171.f2	6171b1	6171.f	6171b	$2$	$2$	\( 3 \cdot 11^{2} \cdot 17 \)	\( 3^{5} \cdot 11^{9} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$1$		$1$	$15840$	$1.420551$	$136590875/70227$	$1.04418$	$4.61908$	$[1, 0, 1, -14281, -220585]$	\(y^2+xy+y=x^3-14281x-220585\)	2.3.0.a.1, 66.6.0.a.1, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[ ]$	$1$
6171.g1	6171d3	6171.g	6171d	$4$	$4$	\( 3 \cdot 11^{2} \cdot 17 \)	\( 3 \cdot 11^{7} \cdot 17^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4488$	$48$	$0$	$4.069722192$	$1$		$0$	$15360$	$1.290005$	$666940371553/2756193$	$0.98070$	$4.76801$	$[1, 0, 1, -22025, 1251743]$	\(y^2+xy+y=x^3-22025x+1251743\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 44.12.0-4.c.1.1, 66.6.0.a.1, $\ldots$	$[(2021/5, -759/5)]$	$1$
6171.g2	6171d2	6171.g	6171d	$4$	$4$	\( 3 \cdot 11^{2} \cdot 17 \)	\( 3^{2} \cdot 11^{8} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2244$	$48$	$0$	$8.139444385$	$1$		$2$	$7680$	$0.943431$	$545338513/314721$	$1.16391$	$3.95346$	$[1, 0, 1, -2060, -2059]$	\(y^2+xy+y=x^3-2060x-2059\)	2.6.0.a.1, 12.12.0-2.a.1.1, 44.12.0-2.a.1.1, 68.12.0.a.1, 132.24.0.?, $\ldots$	$[(63945/8, 15899279/8)]$	$1$
6171.g3	6171d1	6171.g	6171d	$4$	$4$	\( 3 \cdot 11^{2} \cdot 17 \)	\( 3 \cdot 11^{7} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4488$	$48$	$0$	$16.27888877$	$1$		$1$	$3840$	$0.596857$	$192100033/561$	$0.89524$	$3.83391$	$[1, 0, 1, -1455, -21419]$	\(y^2+xy+y=x^3-1455x-21419\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 88.12.0.?, 136.12.0.?, $\ldots$	$[(-24164831/1035, 4927471777/1035)]$	$1$
6171.g4	6171d4	6171.g	6171d	$4$	$4$	\( 3 \cdot 11^{2} \cdot 17 \)	\( - 3^{4} \cdot 11^{10} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4488$	$48$	$0$	$4.069722192$	$1$		$0$	$15360$	$1.290005$	$34741712447/20160657$	$0.99882$	$4.42945$	$[1, 0, 1, 8225, -14401]$	\(y^2+xy+y=x^3+8225x-14401\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 44.12.0-4.c.1.2, 68.12.0.h.1, $\ldots$	$[(61/4, 8195/4)]$	$1$
6171.h1	6171h1	6171.h	6171h	$1$	$1$	\( 3 \cdot 11^{2} \cdot 17 \)	\( - 3^{4} \cdot 11^{7} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$374$	$2$	$0$	$1$	$1$		$0$	$7680$	$0.720111$	$-64000000/15147$	$0.90115$	$3.74726$	$[0, 1, 1, -1008, -14965]$	\(y^2+y=x^3+x^2-1008x-14965\)	374.2.0.?	$[ ]$	$1$
6171.i1	6171i1	6171.i	6171i	$1$	$1$	\( 3 \cdot 11^{2} \cdot 17 \)	\( - 3^{17} \cdot 11^{8} \cdot 17^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$170544$	$2.334801$	$-87367919423488/37321507107$	$1.00339$	$5.93944$	$[0, 1, 1, -553252, 208638403]$	\(y^2+y=x^3+x^2-553252x+208638403\)	6.2.0.a.1	$[ ]$	$1$

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