Elliptic curves over $\Q$ of conductor 305552

Results (30 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	Manin constant
305552.a1	305552a1	305552.a	305552a	$1$	$1$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{14} \cdot 13^{10} \cdot 113 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$452$	$2$	$0$	$9.916323580$	$1$		$0$	$7727616$	$2.028015$	$570375/452$	$0.75943$	$3.73886$	$[0, 0, 0, 142805, 12623962]$	\(y^2=x^3+142805x+12623962\)	452.2.0.?	$[(27791/7, 5698958/7)]$	$1$
305552.b1	305552b1	305552.b	305552b	$1$	$1$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{14} \cdot 13^{4} \cdot 113 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$452$	$2$	$0$	$2.798155147$	$1$		$2$	$594432$	$0.745540$	$570375/452$	$0.75943$	$2.52034$	$[0, 0, 0, 845, 5746]$	\(y^2=x^3+845x+5746\)	452.2.0.?	$[(-1, 70)]$	$1$
305552.c1	305552c1	305552.c	305552c	$1$	$1$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{27} \cdot 13^{7} \cdot 113^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$104$	$2$	$0$	$1$	$1$		$0$	$13547520$	$2.532959$	$9028797181767/5439389696$	$0.95075$	$4.23907$	$[0, 0, 0, 1173029, -99053942]$	\(y^2=x^3+1173029x-99053942\)	104.2.0.?	$[ ]$	$1$
305552.d1	305552d1	305552.d	305552d	$1$	$1$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{25} \cdot 13^{9} \cdot 113 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$11752$	$2$	$0$	$1$	$1$		$0$	$9345024$	$2.508625$	$-11681631109/925696$	$0.85749$	$4.33195$	$[0, 1, 0, -1661664, 878530420]$	\(y^2=x^3+x^2-1661664x+878530420\)	11752.2.0.?	$[ ]$	$1$
305552.e1	305552e1	305552.e	305552e	$2$	$2$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( 2^{12} \cdot 13^{6} \cdot 113 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$11752$	$48$	$0$	$1.018469819$	$1$		$7$	$442368$	$1.099449$	$912673/113$	$0.88900$	$2.96373$	$[0, 1, 0, -5464, 136020]$	\(y^2=x^3+x^2-5464x+136020\)	2.3.0.a.1, 4.6.0.b.1, 104.12.0.?, 226.6.0.?, 452.24.0.?, $\ldots$	$[(4, 338)]$	$1$
305552.e2	305552e2	305552.e	305552e	$2$	$2$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{12} \cdot 13^{6} \cdot 113^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.5	2B	$11752$	$48$	$0$	$2.036939638$	$1$		$5$	$884736$	$1.446022$	$2924207/12769$	$1.12450$	$3.20469$	$[0, 1, 0, 8056, 714676]$	\(y^2=x^3+x^2+8056x+714676\)	2.3.0.a.1, 4.6.0.a.1, 104.12.0.?, 452.12.0.?, 904.24.0.?, $\ldots$	$[(52, 1130)]$	$1$
305552.f1	305552f1	305552.f	305552f	$1$	$1$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{25} \cdot 13^{3} \cdot 113 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$11752$	$2$	$0$	$2.011614706$	$1$		$10$	$718848$	$1.226151$	$-11681631109/925696$	$0.85749$	$3.11343$	$[0, 1, 0, -9832, 396852]$	\(y^2=x^3+x^2-9832x+396852\)	11752.2.0.?	$[(14, 512), (1374/5, 19968/5)]$	$1$
305552.g1	305552g1	305552.g	305552g	$1$	$1$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{14} \cdot 13^{2} \cdot 113 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$452$	$2$	$0$	$6.108655666$	$1$		$2$	$327168$	$0.810700$	$-65804294569/452$	$0.90985$	$3.03706$	$[0, -1, 0, -7440, -244544]$	\(y^2=x^3-x^2-7440x-244544\)	452.2.0.?	$[(850, 24634)]$	$1$
305552.h1	305552h1	305552.h	305552h	$1$	$1$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{31} \cdot 13^{7} \cdot 113^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$104$	$2$	$0$	$3.645946749$	$1$		$2$	$8580096$	$2.762272$	$100149452102519/87030235136$	$0.91687$	$4.42959$	$[0, -1, 0, 2616064, -1154367488]$	\(y^2=x^3-x^2+2616064x-1154367488\)	104.2.0.?	$[(594, 24674)]$	$1$
305552.i1	305552i1	305552.i	305552i	$1$	$1$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{27} \cdot 13^{9} \cdot 113^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$104$	$2$	$0$	$2.479506060$	$1$		$0$	$14515200$	$2.953606$	$201549583253591/919256858624$	$0.93347$	$4.63768$	$[0, -1, 0, 3302880, 6059601664]$	\(y^2=x^3-x^2+3302880x+6059601664\)	104.2.0.?	$[(-4475/2, 248261/2)]$	$1$
305552.j1	305552j1	305552.j	305552j	$1$	$1$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{21} \cdot 13^{9} \cdot 113^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$104$	$2$	$0$	$2.498641193$	$1$		$2$	$27869184$	$3.416004$	$-332019336422194849/183406106683904$	$0.95295$	$5.12448$	$[0, -1, 0, -39007960, -131086264336]$	\(y^2=x^3-x^2-39007960x-131086264336\)	104.2.0.?	$[(100460, 31777408)]$	$1$
305552.k1	305552k1	305552.k	305552k	$1$	$1$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{14} \cdot 13^{8} \cdot 113 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$452$	$2$	$0$	$75.11123073$	$1$		$0$	$4253184$	$2.093174$	$-65804294569/452$	$0.90985$	$4.25557$	$[0, -1, 0, -1257416, -542292752]$	\(y^2=x^3-x^2-1257416x-542292752\)	452.2.0.?	$[(792259409106181122531581013526138/255478562345517, 22200129660145601001610823675443241316605546915170/255478562345517)]$	$1$
305552.l1	305552l2	305552.l	305552l	$2$	$2$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( 2^{8} \cdot 13^{9} \cdot 113^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5876$	$12$	$0$	$1$	$1$		$1$	$1697280$	$1.873629$	$34347024/12769$	$0.87842$	$3.64071$	$[0, 0, 0, -94471, -6683274]$	\(y^2=x^3-94471x-6683274\)	2.3.0.a.1, 26.6.0.b.1, 452.6.0.?, 5876.12.0.?	$[ ]$	$1$
305552.l2	305552l1	305552.l	305552l	$2$	$2$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( 2^{4} \cdot 13^{9} \cdot 113 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5876$	$12$	$0$	$1$	$4$	$2$	$1$	$848640$	$1.527056$	$379275264/113$	$0.90182$	$3.61135$	$[0, 0, 0, -83486, -9282325]$	\(y^2=x^3-83486x-9282325\)	2.3.0.a.1, 52.6.0.c.1, 452.6.0.?, 2938.6.0.?, 5876.12.0.?	$[ ]$	$1$
305552.m1	305552m1	305552.m	305552m	$2$	$2$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( 2^{10} \cdot 13^{6} \cdot 113 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$904$	$12$	$0$	$1$	$1$		$1$	$368640$	$1.038149$	$4630500/113$	$0.84387$	$2.98256$	$[0, 0, 0, -5915, -171366]$	\(y^2=x^3-5915x-171366\)	2.3.0.a.1, 8.6.0.d.1, 226.6.0.?, 904.12.0.?	$[ ]$	$1$
305552.m2	305552m2	305552.m	305552m	$2$	$2$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{11} \cdot 13^{6} \cdot 113^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$904$	$12$	$0$	$1$	$4$	$2$	$1$	$737280$	$1.384722$	$6750/12769$	$1.09106$	$3.16104$	$[0, 0, 0, 845, -540462]$	\(y^2=x^3+845x-540462\)	2.3.0.a.1, 8.6.0.a.1, 452.6.0.?, 904.12.0.?	$[ ]$	$1$
305552.n1	305552n2	305552.n	305552n	$2$	$2$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( 2^{18} \cdot 13^{7} \cdot 113^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5876$	$12$	$0$	$1$	$1$		$1$	$4644864$	$2.610695$	$9677895281132625/10623808$	$0.97805$	$4.79150$	$[0, 0, 0, -12004915, -16009815822]$	\(y^2=x^3-12004915x-16009815822\)	2.3.0.a.1, 26.6.0.b.1, 452.6.0.?, 5876.12.0.?	$[ ]$	$1$
305552.n2	305552n1	305552.n	305552n	$2$	$2$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( 2^{24} \cdot 13^{8} \cdot 113 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5876$	$12$	$0$	$1$	$1$		$1$	$2322432$	$2.264122$	$2419596140625/78221312$	$0.94052$	$4.13481$	$[0, 0, 0, -756275, -245971726]$	\(y^2=x^3-756275x-245971726\)	2.3.0.a.1, 52.6.0.c.1, 226.6.0.?, 5876.12.0.?	$[ ]$	$1$
305552.o1	305552o2	305552.o	305552o	$2$	$2$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( 2^{8} \cdot 13^{3} \cdot 113^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5876$	$12$	$0$	$1$	$1$		$1$	$130560$	$0.591155$	$34347024/12769$	$0.87842$	$2.42220$	$[0, 0, 0, -559, -3042]$	\(y^2=x^3-559x-3042\)	2.3.0.a.1, 26.6.0.b.1, 452.6.0.?, 5876.12.0.?	$[ ]$	$1$
305552.o2	305552o1	305552.o	305552o	$2$	$2$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( 2^{4} \cdot 13^{3} \cdot 113 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5876$	$12$	$0$	$1$	$4$	$2$	$1$	$65280$	$0.244581$	$379275264/113$	$0.90182$	$2.39284$	$[0, 0, 0, -494, -4225]$	\(y^2=x^3-494x-4225\)	2.3.0.a.1, 52.6.0.c.1, 452.6.0.?, 2938.6.0.?, 5876.12.0.?	$[ ]$	$1$
305552.p1	305552p1	305552.p	305552p	$1$	$1$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{13} \cdot 13^{3} \cdot 113^{4} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$104$	$2$	$0$	$4.414136021$	$1$		$6$	$1188864$	$1.814095$	$-63296989903477/326094722$	$0.92707$	$3.78470$	$[0, 1, 0, -172696, -27803372]$	\(y^2=x^3+x^2-172696x-27803372\)	104.2.0.?	$[(846, 20792), (15726/5, 1327976/5)]$	$1$
305552.q1	305552q1	305552.q	305552q	$1$	$1$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{17} \cdot 13^{9} \cdot 113^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$104$	$2$	$0$	$2.209977937$	$1$		$0$	$8386560$	$2.427471$	$-3222118333/408608$	$0.84496$	$4.23549$	$[0, 1, 0, -1081656, 477727316]$	\(y^2=x^3+x^2-1081656x+477727316\)	104.2.0.?	$[(1180/3, 496522/3)]$	$1$
305552.r1	305552r1	305552.r	305552r	$1$	$1$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{17} \cdot 13^{3} \cdot 113^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$104$	$2$	$0$	$1.145720660$	$1$		$4$	$645120$	$1.144999$	$-3222118333/408608$	$0.84496$	$3.01698$	$[0, 1, 0, -6400, 215476]$	\(y^2=x^3+x^2-6400x+215476\)	104.2.0.?	$[(60, 226)]$	$1$
305552.s1	305552s1	305552.s	305552s	$1$	$1$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{13} \cdot 13^{9} \cdot 113^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$104$	$2$	$0$	$1$	$1$		$0$	$15455232$	$3.096569$	$-63296989903477/326094722$	$0.92707$	$5.00322$	$[0, 1, 0, -29185680, -60967265644]$	\(y^2=x^3+x^2-29185680x-60967265644\)	104.2.0.?	$[ ]$	$1$
305552.t1	305552t2	305552.t	305552t	$2$	$2$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( 2^{11} \cdot 13^{7} \cdot 113^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$11752$	$12$	$0$	$9.271930201$	$1$		$1$	$1720320$	$1.722519$	$11222568866/165997$	$0.80813$	$3.65447$	$[0, -1, 0, -100104, -12000496]$	\(y^2=x^3-x^2-100104x-12000496\)	2.3.0.a.1, 104.6.0.?, 452.6.0.?, 11752.12.0.?	$[(196330/21, 51953642/21)]$	$1$
305552.t2	305552t1	305552.t	305552t	$2$	$2$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( 2^{10} \cdot 13^{8} \cdot 113 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$11752$	$12$	$0$	$4.635965100$	$1$		$1$	$860160$	$1.375946$	$40873252/19097$	$0.74341$	$3.15499$	$[0, -1, 0, -12224, 232400]$	\(y^2=x^3-x^2-12224x+232400\)	2.3.0.a.1, 104.6.0.?, 226.6.0.?, 11752.12.0.?	$[(3448/3, 194012/3)]$	$1$
305552.u1	305552u2	305552.u	305552u	$2$	$3$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{15} \cdot 13^{7} \cdot 113^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$35256$	$16$	$0$	$1$	$1$		$0$	$4354560$	$2.307095$	$-3153887529625/150061288$	$0.87169$	$4.16205$	$[0, -1, 0, -826128, 300936128]$	\(y^2=x^3-x^2-826128x+300936128\)	3.4.0.a.1, 156.8.0.?, 2712.8.0.?, 11752.2.0.?, 35256.16.0.?	$[ ]$	$1$
305552.u2	305552u1	305552.u	305552u	$2$	$3$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( - 2^{13} \cdot 13^{9} \cdot 113 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$35256$	$16$	$0$	$1$	$1$		$0$	$1451520$	$1.757788$	$817400375/496522$	$0.83333$	$3.50194$	$[0, -1, 0, 52672, 1019264]$	\(y^2=x^3-x^2+52672x+1019264\)	3.4.0.a.1, 156.8.0.?, 2712.8.0.?, 11752.2.0.?, 35256.16.0.?	$[ ]$	$1$
305552.v1	305552v2	305552.v	305552v	$2$	$2$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( 2^{15} \cdot 13^{6} \cdot 113^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$904$	$12$	$0$	$16.40889984$	$1$		$1$	$2654208$	$1.754776$	$10091699281/102152$	$0.95594$	$3.70094$	$[0, -1, 0, -121736, 16245488]$	\(y^2=x^3-x^2-121736x+16245488\)	2.3.0.a.1, 8.6.0.b.1, 452.6.0.?, 904.12.0.?	$[(173813389/90, 2291171823863/90)]$	$1$
305552.v2	305552v1	305552.v	305552v	$2$	$2$	\( 2^{4} \cdot 13^{2} \cdot 113 \)	\( 2^{18} \cdot 13^{6} \cdot 113 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$904$	$12$	$0$	$8.204449922$	$1$		$1$	$1327104$	$1.408203$	$13997521/7232$	$1.05753$	$3.17991$	$[0, -1, 0, -13576, -194832]$	\(y^2=x^3-x^2-13576x-194832\)	2.3.0.a.1, 8.6.0.c.1, 226.6.0.?, 904.12.0.?	$[(-34667/18, 852605/18)]$	$1$

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