LMFDB - Elliptic curves over $\Q$ of conductor 5733

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Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio

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Results (22 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
5733.a1	5733m1	5733.a	5733m	$1$	$1$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{14} \cdot 7^{13} \cdot 13^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$1$	$1$	$0$	$258048$	$2.712772$	$1811564780171264/11870974573731$	$1.04721$	$6.44032$	$[0, 0, 1, 1119993, -1465824992]$	$y^2+y=x^3+1119993x-1465824992$	182.2.0.?	$[]$
5733.b1	5733b1	5733.b	5733b	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ 3^{3} \cdot 7^{7} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1092$	$12$	$0$	$2.007891786$	$1$	$5$	$1536$	$0.337558$	$421875/91$	$0.93663$	$3.22669$	$[1, -1, 1, -230, -1004]$	$y^2+xy+y=x^3-x^2-230x-1004$	2.3.0.a.1, 12.6.0.c.1, 364.6.0.?, 546.6.0.?, 1092.12.0.?	$[(-8, 20)]$
5733.b2	5733b2	5733.b	5733b	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{3} \cdot 7^{8} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1092$	$12$	$0$	$1.003945893$	$1$	$6$	$3072$	$0.684132$	$4492125/8281$	$0.90809$	$3.59036$	$[1, -1, 1, 505, -6590]$	$y^2+xy+y=x^3-x^2+505x-6590$	2.3.0.a.1, 6.6.0.a.1, 364.6.0.?, 1092.12.0.?	$[(16, 65)]$
5733.c1	5733d1	5733.c	5733d	$2$	$7$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{6} \cdot 7^{4} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$7$	7.24.0.3	7B.6.2	$1092$	$96$	$2$	$1$	$1$	$0$	$1920$	$0.403262$	$-56723625/13$	$1.28311$	$3.72422$	$[1, -1, 1, -965, -11294]$	$y^2+xy+y=x^3-x^2-965x-11294$	7.24.0.b.1, 21.48.0-7.b.1.2, 52.2.0.a.1, 364.48.2.?, 1092.96.2.?	$[]$
5733.c2	5733d2	5733.c	5733d	$2$	$7$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{6} \cdot 7^{4} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$7$	7.24.0.3	7B.6.2	$1092$	$96$	$2$	$1$	$1$	$0$	$13440$	$1.376217$	$11397810375/62748517$	$1.05408$	$4.58443$	$[1, -1, 1, 5650, 475570]$	$y^2+xy+y=x^3-x^2+5650x+475570$	7.24.0.b.1, 21.48.0-7.b.1.1, 52.2.0.a.1, 364.48.2.?, 1092.96.2.?	$[]$
5733.d1	5733k1	5733.d	5733k	$2$	$7$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{6} \cdot 7^{10} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$7$	7.24.0.3	7B.6.2	$1092$	$96$	$2$	$1$	$1$	$0$	$13440$	$1.376217$	$-56723625/13$	$1.28311$	$5.07337$	$[1, -1, 1, -47270, 3968290]$	$y^2+xy+y=x^3-x^2-47270x+3968290$	7.24.0.b.1, 21.48.0-7.b.1.1, 52.2.0.a.1, 364.48.2.?, 1092.96.2.?	$[]$
5733.d2	5733k2	5733.d	5733k	$2$	$7$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{6} \cdot 7^{10} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$7$	7.24.0.3	7B.6.2	$1092$	$96$	$2$	$1$	$1$	$0$	$94080$	$2.349171$	$11397810375/62748517$	$1.05408$	$5.93357$	$[1, -1, 1, 276865, -163674332]$	$y^2+xy+y=x^3-x^2+276865x-163674332$	7.24.0.b.1, 21.48.0-7.b.1.2, 52.2.0.a.1, 364.48.2.?, 1092.96.2.?	$[]$
5733.e1	5733g3	5733.e	5733g	$4$	$4$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ 3^{10} \cdot 7^{6} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2184$	$48$	$0$	$3.777156200$	$1$	$2$	$9216$	$1.203896$	$37159393753/1053$	$1.11616$	$4.92323$	$[1, -1, 1, -30659, -2058514]$	$y^2+xy+y=x^3-x^2-30659x-2058514$	2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 26.6.0.b.1, 52.12.0.g.1, $\ldots$	$[(205, 387)]$
5733.e2	5733g4	5733.e	5733g	$4$	$4$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ 3^{7} \cdot 7^{6} \cdot 13^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2184$	$48$	$0$	$0.944289050$	$1$	$6$	$9216$	$1.203896$	$822656953/85683$	$0.96086$	$4.48292$	$[1, -1, 1, -8609, 280550]$	$y^2+xy+y=x^3-x^2-8609x+280550$	2.3.0.a.1, 4.6.0.c.1, 12.12.0.h.1, 28.12.0-4.c.1.1, 84.24.0.?, $\ldots$	$[(30, 205)]$
5733.e3	5733g2	5733.e	5733g	$4$	$4$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ 3^{8} \cdot 7^{6} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$1092$	$48$	$0$	$1.888578100$	$1$	$8$	$4608$	$0.857321$	$10218313/1521$	$0.91403$	$3.97583$	$[1, -1, 1, -1994, -29032]$	$y^2+xy+y=x^3-x^2-1994x-29032$	2.6.0.a.1, 12.12.0.a.1, 28.12.0-2.a.1.1, 52.12.0.b.1, 84.24.0.?, $\ldots$	$[(-24, 79)]$
5733.e4	5733g1	5733.e	5733g	$4$	$4$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{7} \cdot 7^{6} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2184$	$48$	$0$	$3.777156200$	$1$	$3$	$2304$	$0.510748$	$12167/39$	$0.85844$	$3.37258$	$[1, -1, 1, 211, -2572]$	$y^2+xy+y=x^3-x^2+211x-2572$	2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 28.12.0-4.c.1.2, 78.6.0.?, $\ldots$	$[(34, 190)]$
5733.f1	5733f3	5733.f	5733f	$3$	$9$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{6} \cdot 7^{15} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$1638$	$144$	$3$	$2.065139480$	$1$	$0$	$41472$	$1.882364$	$-178643795968/524596891$	$1.15023$	$5.31314$	$[0, 0, 1, -51744, -11165765]$	$y^2+y=x^3-51744x-11165765$	3.4.0.a.1, 9.12.0.a.1, 21.8.0-3.a.1.1, 63.24.0-9.a.1.1, 78.8.0.?, $\ldots$	$[(9079/5, 529358/5)]$
5733.f2	5733f1	5733.f	5733f	$3$	$9$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{6} \cdot 7^{7} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$1638$	$144$	$3$	$0.229459942$	$1$	$8$	$4608$	$0.783752$	$-43614208/91$	$0.87141$	$4.14394$	$[0, 0, 1, -3234, 70915]$	$y^2+y=x^3-3234x+70915$	3.4.0.a.1, 9.12.0.a.1, 21.8.0-3.a.1.2, 63.24.0-9.a.1.2, 78.8.0.?, $\ldots$	$[(7, 220)]$
5733.f3	5733f2	5733.f	5733f	$3$	$9$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{6} \cdot 7^{9} \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.12.0.1	3Cs	$1638$	$144$	$3$	$0.688379826$	$1$	$4$	$13824$	$1.333059$	$224755712/753571$	$0.95798$	$4.51410$	$[0, 0, 1, 5586, 351832]$	$y^2+y=x^3+5586x+351832$	3.12.0.a.1, 21.24.0-3.a.1.1, 78.24.0.?, 117.36.0.?, 182.2.0.?, $\ldots$	$[(112, 1543)]$
5733.g1	5733e1	5733.g	5733e	$1$	$1$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{12} \cdot 7^{3} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$1.097030007$	$1$	$4$	$1536$	$0.477995$	$32768/9477$	$1.07768$	$3.35553$	$[0, 0, 1, 42, -2340]$	$y^2+y=x^3+42x-2340$	182.2.0.?	$[(14, 31)]$
5733.h1	5733i1	5733.h	5733i	$1$	$1$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{12} \cdot 7^{9} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$1$	$1$	$0$	$10752$	$1.450951$	$32768/9477$	$1.07768$	$4.70467$	$[0, 0, 1, 2058, 802534]$	$y^2+y=x^3+2058x+802534$	182.2.0.?	$[]$
5733.i1	5733c1	5733.i	5733c	$1$	$1$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{10} \cdot 7^{8} \cdot 13^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$52$	$2$	$0$	$1$	$1$	$0$	$32256$	$1.535158$	$17999471/177957$	$0.93225$	$4.81196$	$[1, -1, 0, 8811, 1274454]$	$y^2+xy=x^3-x^2+8811x+1274454$	52.2.0.a.1	$[]$
5733.j1	5733a1	5733.j	5733a	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ 3^{9} \cdot 7^{7} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1092$	$12$	$0$	$4.972029928$	$1$	$1$	$4608$	$0.886864$	$421875/91$	$0.93663$	$3.98838$	$[1, -1, 0, -2067, 29168]$	$y^2+xy=x^3-x^2-2067x+29168$	2.3.0.a.1, 12.6.0.c.1, 364.6.0.?, 546.6.0.?, 1092.12.0.?	$[(928/3, 24284/3)]$
5733.j2	5733a2	5733.j	5733a	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{9} \cdot 7^{8} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1092$	$12$	$0$	$2.486014964$	$1$	$2$	$9216$	$1.233438$	$4492125/8281$	$0.90809$	$4.35205$	$[1, -1, 0, 4548, 173375]$	$y^2+xy=x^3-x^2+4548x+173375$	2.3.0.a.1, 6.6.0.a.1, 364.6.0.?, 1092.12.0.?	$[(394, 7741)]$
5733.k1	5733j1	5733.k	5733j	$1$	$1$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{10} \cdot 7^{2} \cdot 13^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$52$	$2$	$0$	$1$	$1$	$0$	$4608$	$0.562203$	$17999471/177957$	$0.93225$	$3.46282$	$[1, -1, 0, 180, -3767]$	$y^2+xy=x^3-x^2+180x-3767$	52.2.0.a.1	$[]$
5733.l1	5733l1	5733.l	5733l	$1$	$1$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{6} \cdot 7^{7} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$1$	$1$	$0$	$6144$	$0.585932$	$110592/91$	$0.71571$	$3.45283$	$[0, 0, 1, 441, 2315]$	$y^2+y=x^3+441x+2315$	182.2.0.?	$[]$
5733.m1	5733h1	5733.m	5733h	$1$	$1$	$ 3^{2} \cdot 7^{2} \cdot 13 $	$ - 3^{10} \cdot 7^{9} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$1.402519217$	$1$	$0$	$18432$	$1.314049$	$-2019487744/361179$	$0.90207$	$4.61781$	$[0, 0, 1, -11613, 551115]$	$y^2+y=x^3-11613x+551115$	182.2.0.?	$[(161/2, 3083/2)]$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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