Elliptic curve search results

Results (27 matches)

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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
2310.f1	2310f4	2310.f	2310f	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{2} \cdot 3^{5} \cdot 5 \cdot 7^{4} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$9240$	$48$	$0$	$0.132675385$	$1$		$16$	$5120$	$1.196627$	$1953542217204454969/170843779260$	$0.98306$	$5.43785$	$[1, 0, 1, -26044, 1615406]$	\(y^2+xy+y=x^3-26044x+1615406\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 20.12.0-4.c.1.2, 60.24.0-60.h.1.4, $\ldots$	$[(91, -79)]$
6930.bb1	6930bd3	6930.bb	6930bd	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{2} \cdot 3^{11} \cdot 5 \cdot 7^{4} \cdot 11^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$9240$	$48$	$0$	$1$	$4$	$2$	$0$	$40960$	$1.745934$	$1953542217204454969/170843779260$	$0.98306$	$5.50769$	$[1, -1, 1, -234392, -43615969]$	\(y^2+xy+y=x^3-x^2-234392x-43615969\)	2.3.0.a.1, 4.12.0-4.c.1.2, 60.24.0-60.h.1.1, 1848.24.0.?, 3080.24.0.?, $\ldots$	$[ ]$
11550.cc1	11550bu4	11550.cc	11550bu	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{2} \cdot 3^{5} \cdot 5^{7} \cdot 7^{4} \cdot 11^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$9240$	$48$	$0$	$1$	$1$		$2$	$122880$	$2.001347$	$1953542217204454969/170843779260$	$0.98306$	$5.53457$	$[1, 1, 1, -651088, 201925781]$	\(y^2+xy+y=x^3+x^2-651088x+201925781\)	2.3.0.a.1, 4.12.0-4.c.1.1, 60.24.0-60.h.1.3, 1848.24.0.?, 3080.24.0.?, $\ldots$	$[ ]$
16170.p1	16170p3	16170.p	16170p	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \)	\( 2^{2} \cdot 3^{5} \cdot 5 \cdot 7^{10} \cdot 11^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$		$0$	$245760$	$2.169582$	$1953542217204454969/170843779260$	$0.98306$	$5.55073$	$[1, 1, 0, -1276132, -555360476]$	\(y^2+xy=x^3+x^2-1276132x-555360476\)	2.3.0.a.1, 4.6.0.c.1, 60.12.0.h.1, 84.12.0.?, 88.12.0.?, $\ldots$	$[ ]$
18480.m1	18480bu3	18480.m	18480bu	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{14} \cdot 3^{5} \cdot 5 \cdot 7^{4} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$4.922748379$	$1$		$3$	$122880$	$1.889774$	$1953542217204454969/170843779260$	$0.98306$	$5.13352$	$[0, -1, 0, -416696, -103386000]$	\(y^2=x^3-x^2-416696x-103386000\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 20.12.0-4.c.1.1, 60.24.0-60.h.1.2, $\ldots$	$[(2650, 131890)]$
25410.cr1	25410cr4	25410.cr	25410cr	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( 2^{2} \cdot 3^{5} \cdot 5 \cdot 7^{4} \cdot 11^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$2.182041239$	$1$		$4$	$614400$	$2.395573$	$1953542217204454969/170843779260$	$0.98306$	$5.57075$	$[1, 0, 0, -3151266, -2153256984]$	\(y^2+xy=x^3-3151266x-2153256984\)	2.3.0.a.1, 4.6.0.c.1, 56.12.0-4.c.1.5, 60.12.0.h.1, 132.12.0.?, $\ldots$	$[(-1020, 804)]$
34650.bl1	34650y4	34650.bl	34650y	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{2} \cdot 3^{11} \cdot 5^{7} \cdot 7^{4} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1.387052143$	$1$		$6$	$983040$	$2.550652$	$1953542217204454969/170843779260$	$0.98306$	$5.58349$	$[1, -1, 0, -5859792, -5457855884]$	\(y^2+xy=x^3-x^2-5859792x-5457855884\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 20.12.0-4.c.1.1, 60.24.0-60.h.1.2, $\ldots$	$[(-1402, 134)]$
48510.cj1	48510cs4	48510.cj	48510cs	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \)	\( 2^{2} \cdot 3^{11} \cdot 5 \cdot 7^{10} \cdot 11^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$		$0$	$1966080$	$2.718887$	$1953542217204454969/170843779260$	$0.98306$	$5.59648$	$[1, -1, 1, -11485193, 14983247661]$	\(y^2+xy+y=x^3-x^2-11485193x+14983247661\)	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.1, 60.12.0.h.1, 264.12.0.?, $\ldots$	$[ ]$
55440.eq1	55440eu4	55440.eq	55440eu	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{14} \cdot 3^{11} \cdot 5 \cdot 7^{4} \cdot 11^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$9240$	$48$	$0$	$1$	$1$		$3$	$983040$	$2.439079$	$1953542217204454969/170843779260$	$0.98306$	$5.22066$	$[0, 0, 0, -3750267, 2795172266]$	\(y^2=x^3-3750267x+2795172266\)	2.3.0.a.1, 4.12.0-4.c.1.1, 60.24.0-60.h.1.3, 1848.24.0.?, 3080.24.0.?, $\ldots$	$[ ]$
73920.cl1	73920y4	73920.cl	73920y	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{20} \cdot 3^{5} \cdot 5 \cdot 7^{4} \cdot 11^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$		$1$	$983040$	$2.236347$	$1953542217204454969/170843779260$	$0.98306$	$4.86969$	$[0, -1, 0, -1666785, 828754785]$	\(y^2=x^3-x^2-1666785x+828754785\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 40.12.0-4.c.1.2, 60.12.0.h.1, $\ldots$	$[ ]$
73920.ij1	73920ii4	73920.ij	73920ii	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{20} \cdot 3^{5} \cdot 5 \cdot 7^{4} \cdot 11^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$		$1$	$983040$	$2.236347$	$1953542217204454969/170843779260$	$0.98306$	$4.86969$	$[0, 1, 0, -1666785, -828754785]$	\(y^2=x^3+x^2-1666785x-828754785\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 40.12.0-4.c.1.1, 60.12.0.h.1, $\ldots$	$[ ]$
76230.cl1	76230cj4	76230.cl	76230cj	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( 2^{2} \cdot 3^{11} \cdot 5 \cdot 7^{4} \cdot 11^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1.990349558$	$1$		$4$	$4915200$	$2.944881$	$1953542217204454969/170843779260$	$0.98306$	$5.61270$	$[1, -1, 0, -28361394, 58137938568]$	\(y^2+xy=x^3-x^2-28361394x+58137938568\)	2.3.0.a.1, 4.6.0.c.1, 44.12.0-4.c.1.1, 60.12.0.h.1, 168.12.0.?, $\ldots$	$[(2764, 27900)]$
80850.gw1	80850gm4	80850.gw	80850gm	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{2} \cdot 3^{5} \cdot 5^{7} \cdot 7^{10} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$2.448510421$	$1$		$4$	$5898240$	$2.974300$	$1953542217204454969/170843779260$	$0.98306$	$5.61472$	$[1, 0, 0, -31903313, -69356252883]$	\(y^2+xy=x^3-31903313x-69356252883\)	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 60.12.0.h.1, 264.12.0.?, $\ldots$	$[(-3254, 3805)]$
92400.fa1	92400gc4	92400.fa	92400gc	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{14} \cdot 3^{5} \cdot 5^{7} \cdot 7^{4} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$9240$	$48$	$0$	$2.330087701$	$1$		$7$	$2949120$	$2.694492$	$1953542217204454969/170843779260$	$0.98306$	$5.25548$	$[0, 1, 0, -10417408, -12944084812]$	\(y^2=x^3+x^2-10417408x-12944084812\)	2.3.0.a.1, 4.12.0-4.c.1.2, 60.24.0-60.h.1.1, 1848.24.0.?, 3080.24.0.?, $\ldots$	$[(-1852, 450)]$
127050.i1	127050e4	127050.i	127050e	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( 2^{2} \cdot 3^{5} \cdot 5^{7} \cdot 7^{4} \cdot 11^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$		$0$	$14745600$	$3.200294$	$1953542217204454969/170843779260$	$0.98306$	$5.62953$	$[1, 1, 0, -78781650, -269157123000]$	\(y^2+xy=x^3+x^2-78781650x-269157123000\)	2.3.0.a.1, 4.6.0.c.1, 44.12.0-4.c.1.2, 60.12.0.h.1, 168.12.0.?, $\ldots$	$[ ]$
129360.gs1	129360hh4	129360.gs	129360hh	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \)	\( 2^{14} \cdot 3^{5} \cdot 5 \cdot 7^{10} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$2.775835029$	$1$		$5$	$5898240$	$2.862728$	$1953542217204454969/170843779260$	$0.98306$	$5.27677$	$[0, 1, 0, -20418120, 35502234228]$	\(y^2=x^3+x^2-20418120x+35502234228\)	2.3.0.a.1, 4.6.0.c.1, 60.12.0.h.1, 84.12.0.?, 88.12.0.?, $\ldots$	$[(2748, 12342)]$
177870.gb1	177870cs3	177870.gb	177870cs	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( 2^{2} \cdot 3^{5} \cdot 5 \cdot 7^{10} \cdot 11^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$9240$	$48$	$0$	$12.19768262$	$1$		$0$	$29491200$	$3.368530$	$1953542217204454969/170843779260$	$0.98306$	$5.63985$	$[1, 1, 1, -154412035, 738412733477]$	\(y^2+xy+y=x^3+x^2-154412035x+738412733477\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 60.12.0.h.1, 120.24.0.?, $\ldots$	$[(55505875/87, 12240249728/87)]$
203280.x1	203280eh3	203280.x	203280eh	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( 2^{14} \cdot 3^{5} \cdot 5 \cdot 7^{4} \cdot 11^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$11.10431445$	$1$		$1$	$14745600$	$3.088722$	$1953542217204454969/170843779260$	$0.98306$	$5.30351$	$[0, -1, 0, -50420256, 137808446976]$	\(y^2=x^3-x^2-50420256x+137808446976\)	2.3.0.a.1, 4.6.0.c.1, 56.12.0-4.c.1.5, 60.12.0.h.1, 132.12.0.?, $\ldots$	$[(2189141/23, 33781090/23)]$
221760.cu1	221760lr4	221760.cu	221760lr	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{20} \cdot 3^{11} \cdot 5 \cdot 7^{4} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$9240$	$48$	$0$	$2.621813942$	$1$		$3$	$7864320$	$2.785652$	$1953542217204454969/170843779260$	$0.98306$	$4.97057$	$[0, 0, 0, -15001068, -22361378128]$	\(y^2=x^3-15001068x-22361378128\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 60.12.0.h.1, 120.24.0.?, $\ldots$	$[(8902, 741312)]$
221760.ek1	221760ee3	221760.ek	221760ee	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{20} \cdot 3^{11} \cdot 5 \cdot 7^{4} \cdot 11^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$9240$	$48$	$0$	$1$	$1$		$1$	$7864320$	$2.785652$	$1953542217204454969/170843779260$	$0.98306$	$4.97057$	$[0, 0, 0, -15001068, 22361378128]$	\(y^2=x^3-15001068x+22361378128\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 60.12.0.h.1, 120.24.0.?, $\ldots$	$[ ]$
242550.be1	242550be3	242550.be	242550be	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{2} \cdot 3^{11} \cdot 5^{7} \cdot 7^{10} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1.688994333$	$1$		$6$	$47185920$	$3.523605$	$1953542217204454969/170843779260$	$0.98306$	$5.64885$	$[1, -1, 0, -287129817, 1872618827841]$	\(y^2+xy=x^3-x^2-287129817x+1872618827841\)	2.3.0.a.1, 4.6.0.c.1, 60.12.0.h.1, 84.12.0.?, 88.12.0.?, $\ldots$	$[(9424, 55313)]$
277200.fm1	277200fm3	277200.fm	277200fm	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{14} \cdot 3^{11} \cdot 5^{7} \cdot 7^{4} \cdot 11^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$		$1$	$23592960$	$3.243797$	$1953542217204454969/170843779260$	$0.98306$	$5.32075$	$[0, 0, 0, -93756675, 349396533250]$	\(y^2=x^3-93756675x+349396533250\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 20.12.0-4.c.1.2, 60.24.0-60.h.1.4, $\ldots$	$[ ]$
369600.ed1	369600ed4	369600.ed	369600ed	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{20} \cdot 3^{5} \cdot 5^{7} \cdot 7^{4} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$9240$	$48$	$0$	$13.88480076$	$1$		$1$	$23592960$	$3.041065$	$1953542217204454969/170843779260$	$0.98306$	$5.01159$	$[0, -1, 0, -41669633, -103511008863]$	\(y^2=x^3-x^2-41669633x-103511008863\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 60.12.0.h.1, 120.24.0.?, $\ldots$	$[(36881368/13, 223881030625/13)]$
369600.rv1	369600rv3	369600.rv	369600rv	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{20} \cdot 3^{5} \cdot 5^{7} \cdot 7^{4} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$9240$	$48$	$0$	$0.890847914$	$1$		$9$	$23592960$	$3.041065$	$1953542217204454969/170843779260$	$0.98306$	$5.01159$	$[0, 1, 0, -41669633, 103511008863]$	\(y^2=x^3+x^2-41669633x+103511008863\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 60.12.0.h.1, 120.24.0.?, $\ldots$	$[(3403, 33600)]$
381150.kb1	381150kb3	381150.kb	381150kb	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( 2^{2} \cdot 3^{11} \cdot 5^{7} \cdot 7^{4} \cdot 11^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$		$0$	$117964800$	$3.749599$	$1953542217204454969/170843779260$	$0.98306$	$5.66120$	$[1, -1, 1, -709034855, 7266533286147]$	\(y^2+xy+y=x^3-x^2-709034855x+7266533286147\)	2.3.0.a.1, 4.6.0.c.1, 56.12.0-4.c.1.3, 60.12.0.h.1, 132.12.0.?, $\ldots$	$[ ]$
388080.gf1	388080gf4	388080.gf	388080gf	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \)	\( 2^{14} \cdot 3^{11} \cdot 5 \cdot 7^{10} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$12.68662841$	$1$		$1$	$47185920$	$3.412037$	$1953542217204454969/170843779260$	$0.98306$	$5.33851$	$[0, 0, 0, -183763083, -958744087238]$	\(y^2=x^3-183763083x-958744087238\)	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 60.12.0.h.1, 264.12.0.?, $\ldots$	$[(23169727/33, 78427152370/33)]$
390390.ev1	390390ev3	390390.ev	390390ev	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13^{2} \)	\( 2^{2} \cdot 3^{5} \cdot 5 \cdot 7^{4} \cdot 11^{4} \cdot 13^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$120120$	$48$	$0$	$1.669674452$	$1$		$4$	$11796480$	$2.479103$	$1953542217204454969/170843779260$	$0.98306$	$4.46651$	$[1, 0, 0, -4401355, 3553448885]$	\(y^2+xy=x^3-4401355x+3553448885\)	2.3.0.a.1, 4.6.0.c.1, 60.12.0.h.1, 156.12.0.?, 260.12.0.?, $\ldots$	$[(1262, 2411)]$

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