Elliptic curves over $\Q$ of conductor 234

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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
234.a1	234c2	234.a	234c	$2$	$2$	\( 2 \cdot 3^{2} \cdot 13 \)	\( 2^{2} \cdot 3^{3} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.138579856$	$1$		$14$	$32$	$-0.242657$	$1033364331/676$	$1.11849$	$4.40889$	$[1, -1, 0, -63, 209]$	\(y^2+xy=x^3-x^2-63x+209\)	2.3.0.a.1, 12.6.0.a.1, 52.6.0.e.1, 156.12.0.?	$[(8, 9)]$
234.a2	234c1	234.a	234c	$2$	$2$	\( 2 \cdot 3^{2} \cdot 13 \)	\( - 2^{4} \cdot 3^{3} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.277159712$	$1$		$9$	$16$	$-0.589231$	$-132651/208$	$1.11492$	$3.00665$	$[1, -1, 0, -3, 5]$	\(y^2+xy=x^3-x^2-3x+5\)	2.3.0.a.1, 12.6.0.b.1, 52.6.0.e.1, 78.6.0.?, 156.12.0.?	$[(1, 1)]$
234.b1	234a2	234.b	234a	$2$	$7$	\( 2 \cdot 3^{2} \cdot 13 \)	\( - 2 \cdot 3^{6} \cdot 13^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$2184$	$96$	$2$	$1$	$1$		$0$	$196$	$0.839101$	$-1064019559329/125497034$	$1.06269$	$6.31865$	$[1, -1, 0, -1914, 35846]$	\(y^2+xy=x^3-x^2-1914x+35846\)	7.24.0.a.2, 21.48.0-7.a.2.2, 104.2.0.?, 728.48.2.?, 2184.96.2.?	$[]$
234.b2	234a1	234.b	234a	$2$	$7$	\( 2 \cdot 3^{2} \cdot 13 \)	\( - 2^{7} \cdot 3^{6} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.1	7B.6.1	$2184$	$96$	$2$	$1$	$1$		$0$	$28$	$-0.133854$	$-2146689/1664$	$0.96784$	$4.03661$	$[1, -1, 0, -24, -64]$	\(y^2+xy=x^3-x^2-24x-64\)	7.24.0.a.1, 21.48.0-7.a.1.2, 104.2.0.?, 728.48.2.?, 2184.96.2.?	$[]$
234.c1	234d3	234.c	234d	$4$	$4$	\( 2 \cdot 3^{2} \cdot 13 \)	\( 2^{4} \cdot 3^{11} \cdot 13^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$312$	$48$	$0$	$1$	$1$		$0$	$1280$	$1.517384$	$986551739719628473/111045168$	$1.06555$	$8.80327$	$[1, -1, 1, -186656, -30992493]$	\(y^2+xy+y=x^3-x^2-186656x-30992493\)	2.3.0.a.1, 4.12.0-4.c.1.2, 12.24.0-12.h.1.1, 104.24.0.?, 312.48.0.?	$[]$
234.c2	234d4	234.c	234d	$4$	$4$	\( 2 \cdot 3^{2} \cdot 13 \)	\( 2^{4} \cdot 3^{26} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$312$	$48$	$0$	$1$	$1$		$0$	$1280$	$1.517384$	$1416134368422073/725251155408$	$1.07849$	$7.60329$	$[1, -1, 1, -21056, 404115]$	\(y^2+xy+y=x^3-x^2-21056x+404115\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.1, 24.24.0-24.ba.1.12, $\ldots$	$[]$
234.c3	234d2	234.c	234d	$4$	$4$	\( 2 \cdot 3^{2} \cdot 13 \)	\( 2^{8} \cdot 3^{16} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$156$	$48$	$0$	$1$	$1$		$2$	$640$	$1.170811$	$242702053576633/2554695936$	$1.10395$	$7.27996$	$[1, -1, 1, -11696, -479469]$	\(y^2+xy+y=x^3-x^2-11696x-479469\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.2, 52.24.0-52.b.1.3, 156.48.0.?	$[]$
234.c4	234d1	234.c	234d	$4$	$4$	\( 2 \cdot 3^{2} \cdot 13 \)	\( - 2^{16} \cdot 3^{11} \cdot 13 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$312$	$48$	$0$	$1$	$1$		$3$	$320$	$0.824237$	$-822656953/207028224$	$1.08584$	$6.08526$	$[1, -1, 1, -176, -18669]$	\(y^2+xy+y=x^3-x^2-176x-18669\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.ba.1.8, 78.6.0.?, 104.24.0.?, $\ldots$	$[]$
234.d1	234b2	234.d	234b	$2$	$2$	\( 2 \cdot 3^{2} \cdot 13 \)	\( 2^{2} \cdot 3^{9} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$0$	$96$	$0.306649$	$1033364331/676$	$1.11849$	$5.61719$	$[1, -1, 1, -569, -5075]$	\(y^2+xy+y=x^3-x^2-569x-5075\)	2.3.0.a.1, 12.6.0.a.1, 52.6.0.e.1, 156.12.0.?	$[]$
234.d2	234b1	234.d	234b	$2$	$2$	\( 2 \cdot 3^{2} \cdot 13 \)	\( - 2^{4} \cdot 3^{9} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$48$	$-0.039925$	$-132651/208$	$1.11492$	$4.21495$	$[1, -1, 1, -29, -107]$	\(y^2+xy+y=x^3-x^2-29x-107\)	2.3.0.a.1, 12.6.0.b.1, 52.6.0.e.1, 78.6.0.?, 156.12.0.?	$[]$
234.e1	234e3	234.e	234e	$3$	$9$	\( 2 \cdot 3^{2} \cdot 13 \)	\( - 2^{9} \cdot 3^{6} \cdot 13 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	9.24.0.1	3B.1.1	$936$	$144$	$3$	$1$	$1$		$2$	$180$	$0.603693$	$-10730978619193/6656$	$1.02193$	$6.70828$	$[1, -1, 1, -4136, 103403]$	\(y^2+xy+y=x^3-x^2-4136x+103403\)	3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 104.2.0.?, 117.72.0.?, 312.16.0.?, $\ldots$	$[]$
234.e2	234e2	234.e	234e	$3$	$9$	\( 2 \cdot 3^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{6} \cdot 13^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.24.0.1	3Cs.1.1	$936$	$144$	$3$	$1$	$1$		$2$	$60$	$0.054386$	$-10218313/17576$	$0.94717$	$4.41967$	$[1, -1, 1, -41, 209]$	\(y^2+xy+y=x^3-x^2-41x+209\)	3.24.0-3.a.1.1, 104.2.0.?, 117.72.0.?, 312.48.1.?, 936.144.3.?	$[]$
234.e3	234e1	234.e	234e	$3$	$9$	\( 2 \cdot 3^{2} \cdot 13 \)	\( - 2 \cdot 3^{6} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.24.0.3	3B.1.2	$936$	$144$	$3$	$1$	$1$		$0$	$20$	$-0.494920$	$12167/26$	$0.84415$	$3.11415$	$[1, -1, 1, 4, -7]$	\(y^2+xy+y=x^3-x^2+4x-7\)	3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 104.2.0.?, 117.72.0.?, 312.16.0.?, $\ldots$	$[]$

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