Elliptic curves over $\Q$ of conductor 59643

The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

Results (18 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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
59643.a1	59643m1	59643.a	59643m	$1$	$1$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{3} \cdot 47^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$0.905330859$	$1$		$4$	$2967552$	$2.460056$	$-432081216000000/2209$	$1.17586$	$5.46523$	$1$	$[0, 0, 1, -10437525, 12979094920]$	\(y^2+y=x^3-10437525x+12979094920\)	6.2.0.a.1	$[(1880, 1104)]$	$1$
59643.b1	59643l1	59643.b	59643l	$1$	$1$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{11} \cdot 47^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$10.61864285$	$1$		$0$	$1271808$	$2.259365$	$1536000/2209$	$0.82875$	$4.53121$	$1$	$[0, 0, 1, 298215, 76387772]$	\(y^2+y=x^3+298215x+76387772\)	6.2.0.a.1	$[(1776835/21, 2391506263/21)]$	$1$
59643.c1	59643h1	59643.c	59643h	$1$	$1$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{11} \cdot 47^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓				$6$	$2$	$0$	$2.768759070$	$1$		$2$	$15552$	$0.330375$	$141$	$0.72414$	$2.46947$	$1$	$[1, -1, 1, 79, 892]$	\(y^2+xy+y=x^3-x^2+79x+892\)	6.2.0.a.1	$[(2, 31)]$	$1$
59643.d1	59643g1	59643.d	59643g	$1$	$1$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{11} \cdot 47^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓				$6$	$2$	$0$	$13.20098930$	$1$		$0$	$730944$	$2.255447$	$141$	$0.72414$	$4.57029$	$1$	$[1, -1, 1, 175201, -94740110]$	\(y^2+xy+y=x^3-x^2+175201x-94740110\)	6.2.0.a.1	$[(70902514/255, 609554764552/255)]$	$1$
59643.e1	59643i1	59643.e	59643i	$1$	$1$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{9} \cdot 47^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$564$	$2$	$0$	$4.154997836$	$1$		$0$	$397440$	$1.780836$	$-132651/47$	$0.75661$	$4.11613$	$1$	$[1, -1, 1, -63371, -7780616]$	\(y^2+xy+y=x^3-x^2-63371x-7780616\)	564.2.0.?	$[(9136/5, 503944/5)]$	$1$
59643.f1	59643d4	59643.f	59643d	$4$	$27$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{11} \cdot 47^{6} \)	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-27$	$N(\mathrm{U}(1))$		✓							$4.692411943$	$1$		$0$	$317952$	$1.977222$	$-12288000$	$1.23864$	$4.68436$	$1$	$[0, 0, 1, -596430, 177303728]$	\(y^2+y=x^3-596430x+177303728\)		$[(16873/6, 183239/6)]$	$1$
59643.f2	59643d2	59643.f	59643d	$4$	$27$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{5} \cdot 47^{6} \)	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-27$	$N(\mathrm{U}(1))$		✓							$14.07723582$	$1$		$0$	$105984$	$1.427916$	$-12288000$	$1.23864$	$4.08491$	$1$	$[0, 0, 1, -66270, -6566805]$	\(y^2+y=x^3-66270x-6566805\)		$[(40713609/370, 8436585977/370)]$	$1$
59643.f3	59643d1	59643.f	59643d	$4$	$27$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{3} \cdot 47^{6} \)	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3$	27.972.55.16	3Cs				$4.692411943$	$1$		$0$	$35328$	$0.878610$	$0$		$3.07849$	$1$	$[0, 0, 1, 0, -25956]$	\(y^2+y=x^3-25956\)		$[(2961/10, 1709/10)]$	$1$
59643.f4	59643d3	59643.f	59643d	$4$	$27$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{9} \cdot 47^{6} \)	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3$	27.972.55.16	3Cs				$1.564137314$	$1$		$0$	$105984$	$1.427916$	$0$		$3.67794$	$1$	$[0, 0, 1, 0, 700805]$	\(y^2+y=x^3+700805\)		$[(705/2, 19877/2)]$	$1$
59643.g1	59643b1	59643.g	59643b	$2$	$3$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{3} \cdot 47^{2} \)	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$0$	$4944$	$-0.404773$	$0$		$1.67794$	$1$	$[0, 0, 1, 0, -12]$	\(y^2+y=x^3-12\)		$[ ]$	$1$
59643.g2	59643b2	59643.g	59643b	$2$	$3$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{9} \cdot 47^{2} \)	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$0$	$14832$	$0.144533$	$0$		$2.27739$	$1$	$[0, 0, 1, 0, 317]$	\(y^2+y=x^3+317\)		$[ ]$	$1$
59643.h1	59643a2	59643.h	59643a	$2$	$3$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{9} \cdot 47^{8} \)	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3$	27.648.18.4	3B.1.2				$1$	$25$	$5$	$0$	$697104$	$2.069607$	$0$		$4.37821$	$1$	$[0, 0, 1, 0, -32937847]$	\(y^2+y=x^3-32937847\)		$[ ]$	$1$
59643.h2	59643a1	59643.h	59643a	$2$	$3$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{3} \cdot 47^{8} \)	$0$	$\Z/3\Z$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3$	27.648.18.1	3B.1.1				$1$	$25$	$5$	$2$	$232368$	$1.520300$	$0$		$3.77876$	$1$	$[0, 0, 1, 0, 1219920]$	\(y^2+y=x^3+1219920\)		$[ ]$	$1$
59643.i1	59643c1	59643.i	59643c	$1$	$1$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{3} \cdot 47^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$564$	$2$	$0$	$1$	$1$		$0$	$132480$	$1.231529$	$-132651/47$	$0.75661$	$3.51668$	$1$	$[1, -1, 0, -7041, 290518]$	\(y^2+xy=x^3-x^2-7041x+290518\)	564.2.0.?	$[ ]$	$1$
59643.j1	59643f1	59643.j	59643f	$1$	$1$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{5} \cdot 47^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓				$6$	$2$	$0$	$23.50706622$	$1$		$0$	$243648$	$1.706142$	$141$	$0.72414$	$3.97084$	$1$	$[1, -1, 0, 19467, 3502404]$	\(y^2+xy=x^3-x^2+19467x+3502404\)	6.2.0.a.1	$[(-7468764416/8263, 163186736988194/8263)]$	$1$
59643.k1	59643e1	59643.k	59643e	$1$	$1$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{5} \cdot 47^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓				$6$	$2$	$0$	$6.644375917$	$1$		$0$	$5184$	$-0.218931$	$141$	$0.72414$	$1.87002$	$1$	$[1, -1, 0, 9, -36]$	\(y^2+xy=x^3-x^2+9x-36\)	6.2.0.a.1	$[(724/5, 17508/5)]$	$1$
59643.l1	59643k1	59643.l	59643k	$1$	$1$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{9} \cdot 47^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$75.13375632$	$1$		$0$	$8902656$	$3.009361$	$-432081216000000/2209$	$1.17586$	$6.06468$	$1$	$[0, 0, 1, -93937725, -350435562847]$	\(y^2+y=x^3-93937725x-350435562847\)	6.2.0.a.1	$[(76009954228403854510953136622731281/1387529323539430, 20252958138201448664369244780731747294291914083028429/1387529323539430)]$	$1$
59643.m1	59643j1	59643.m	59643j	$1$	$1$	\( 3^{3} \cdot 47^{2} \)	\( - 3^{5} \cdot 47^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$31.16337043$	$1$		$0$	$423936$	$1.710058$	$1536000/2209$	$0.82875$	$3.93176$	$1$	$[0, 0, 1, 33135, -2829177]$	\(y^2+y=x^3+33135x-2829177\)	6.2.0.a.1	$[(1595780541659217/359542, 63753858505987363944315/359542)]$	$1$

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