Elliptic curves over $\Q$ of conductor 147

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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
147.a1	147a5	147.a	147a	$6$	$8$	\( 3 \cdot 7^{2} \)	\( 3 \cdot 7^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.174	2B	$336$	$192$	$1$	$1$	$1$		$0$	$192$	$1.047161$	$53297461115137/147$	$1.05087$	$8.67307$	$[1, 1, 1, -38417, 2882228]$	\(y^2+xy+y=x^3+x^2-38417x+2882228\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.3, 12.12.0.h.1, 16.48.0-16.e.2.3, $\ldots$	$[]$
147.a2	147a4	147.a	147a	$6$	$8$	\( 3 \cdot 7^{2} \)	\( 3^{2} \cdot 7^{10} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.109	2Cs	$168$	$192$	$1$	$1$	$1$		$2$	$96$	$0.700587$	$13027640977/21609$	$1.08149$	$7.00657$	$[1, 1, 1, -2402, 44246]$	\(y^2+xy+y=x^3+x^2-2402x+44246\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.e.1.10, 12.24.0.c.1, 24.96.0-24.j.2.15, $\ldots$	$[]$
147.a3	147a3	147.a	147a	$6$	$8$	\( 3 \cdot 7^{2} \)	\( 3^{8} \cdot 7^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.182	2B	$336$	$192$	$1$	$1$	$1$		$0$	$96$	$0.700587$	$6570725617/45927$	$1.00160$	$6.86941$	$[1, 1, 1, -1912, -32782]$	\(y^2+xy+y=x^3+x^2-1912x-32782\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.1.6, 28.24.0-28.h.1.1, 48.96.0-48.bf.1.10, $\ldots$	$[]$
147.a4	147a6	147.a	147a	$6$	$8$	\( 3 \cdot 7^{2} \)	\( - 3 \cdot 7^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.125	2B	$336$	$192$	$1$	$1$	$1$		$0$	$192$	$1.047161$	$-4354703137/17294403$	$1.04266$	$7.20020$	$[1, 1, 1, -1667, 72764]$	\(y^2+xy+y=x^3+x^2-1667x+72764\)	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.bb.2, 12.12.0.g.1, $\ldots$	$[]$
147.a5	147a2	147.a	147a	$6$	$8$	\( 3 \cdot 7^{2} \)	\( 3^{4} \cdot 7^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.11	2Cs	$168$	$192$	$1$	$1$	$1$		$2$	$48$	$0.354013$	$7189057/3969$	$1.14862$	$5.50324$	$[1, 1, 1, -197, 146]$	\(y^2+xy+y=x^3+x^2-197x+146\)	2.6.0.a.1, 4.24.0-4.b.1.2, 8.48.0-8.e.2.15, 24.96.0-24.w.2.15, 28.48.0-28.c.1.4, $\ldots$	$[]$
147.a6	147a1	147.a	147a	$6$	$8$	\( 3 \cdot 7^{2} \)	\( - 3^{2} \cdot 7^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.33	2B	$336$	$192$	$1$	$1$	$1$		$3$	$24$	$0.007440$	$103823/63$	$0.97868$	$4.65409$	$[1, 1, 1, 48, 48]$	\(y^2+xy+y=x^3+x^2+48x+48\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.12, 14.6.0.b.1, 16.48.0-16.e.1.15, $\ldots$	$[]$
147.b1	147c2	147.b	147c	$2$	$13$	\( 3 \cdot 7^{2} \)	\( - 3^{13} \cdot 7^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$13$	13.28.0.2	13B.4.2	$546$	$336$	$9$	$1$	$1$		$0$	$78$	$0.437387$	$-1713910976512/1594323$	$1.10592$	$6.42494$	$[0, -1, 1, -912, 10919]$	\(y^2+y=x^3-x^2-912x+10919\)	6.2.0.a.1, 13.28.0.a.2, 78.56.1.?, 91.168.2.?, 546.336.9.?	$[]$
147.b2	147c1	147.b	147c	$2$	$13$	\( 3 \cdot 7^{2} \)	\( - 3 \cdot 7^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$13$	13.28.0.1	13B.4.1	$546$	$336$	$9$	$1$	$1$		$0$	$6$	$-0.845087$	$-28672/3$	$0.91239$	$2.86983$	$[0, -1, 1, -2, -1]$	\(y^2+y=x^3-x^2-2x-1\)	6.2.0.a.1, 13.28.0.a.1, 78.56.1.?, 91.168.2.?, 546.336.9.?	$[]$
147.c1	147b2	147.c	147b	$2$	$13$	\( 3 \cdot 7^{2} \)	\( - 3^{13} \cdot 7^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$13$	13.56.0.3	13B.3.2	$546$	$336$	$9$	$1$	$1$		$0$	$546$	$1.410343$	$-1713910976512/1594323$	$1.10592$	$8.76451$	$[0, 1, 1, -44704, -3655907]$	\(y^2+y=x^3+x^2-44704x-3655907\)	6.2.0.a.1, 13.56.0-13.a.2.2, 78.112.1.?, 91.168.2.?, 546.336.9.?	$[]$
147.c2	147b1	147.c	147b	$2$	$13$	\( 3 \cdot 7^{2} \)	\( - 3 \cdot 7^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$13$	13.56.0.1	13B.3.1	$546$	$336$	$9$	$1$	$1$		$0$	$42$	$0.127867$	$-28672/3$	$0.91239$	$5.20940$	$[0, 1, 1, -114, 473]$	\(y^2+y=x^3+x^2-114x+473\)	6.2.0.a.1, 13.56.0-13.a.1.1, 78.112.1.?, 91.168.2.?, 546.336.9.?	$[]$

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