LMFDB - Elliptic curve search results

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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	Manin constant

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Results (20 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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
7098.l1	7098h2	7098.l	7098h	$2$	$3$	$ 2 \cdot 3 \cdot 7 \cdot 13^{2} $	$ 2 \cdot 3 \cdot 7^{3} \cdot 13^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2184$	$16$	$0$	$1$	$9$	$3$	$0$	$78624$	$1.986570$	$531373116625/2058$	$0.99657$	$5.93717$	$[1, 0, 1, -871706, -313330054]$	$y^2+xy+y=x^3-871706x-313330054$	3.4.0.a.1, 39.8.0-3.a.1.2, 168.8.0.?, 2184.16.0.?	$[ ]$
7098.bb1	7098ba2	7098.bb	7098ba	$2$	$3$	$ 2 \cdot 3 \cdot 7 \cdot 13^{2} $	$ 2 \cdot 3 \cdot 7^{3} \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$168$	$16$	$0$	$1$	$1$		$0$	$6048$	$0.704096$	$531373116625/2058$	$0.99657$	$4.20166$	$[1, 0, 0, -5158, -143014]$	$y^2+xy=x^3-5158x-143014$	3.8.0-3.a.1.1, 168.16.0.?	$[ ]$
21294.u1	21294bc2	21294.u	21294bc	$2$	$3$	$ 2 \cdot 3^{2} \cdot 7 \cdot 13^{2} $	$ 2 \cdot 3^{7} \cdot 7^{3} \cdot 13^{4} $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$168$	$16$	$0$	$1.791330823$	$1$		$6$	$48384$	$1.253401$	$531373116625/2058$	$0.99657$	$4.39990$	$[1, -1, 0, -46422, 3861378]$	$y^2+xy=x^3-x^2-46422x+3861378$	3.8.0-3.a.1.2, 168.16.0.?	$[(123, -30)]$
21294.ce1	21294ca2	21294.ce	21294ca	$2$	$3$	$ 2 \cdot 3^{2} \cdot 7 \cdot 13^{2} $	$ 2 \cdot 3^{7} \cdot 7^{3} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2184$	$16$	$0$	$13.94304861$	$1$		$0$	$628992$	$2.535877$	$531373116625/2058$	$0.99657$	$5.94409$	$[1, -1, 1, -7845350, 8459911451]$	$y^2+xy+y=x^3-x^2-7845350x+8459911451$	3.4.0.a.1, 39.8.0-3.a.1.1, 168.8.0.?, 2184.16.0.?	$[(733485/44, 6325223573/44)]$
49686.l1	49686f2	49686.l	49686f	$2$	$3$	$ 2 \cdot 3 \cdot 7^{2} \cdot 13^{2} $	$ 2 \cdot 3 \cdot 7^{9} \cdot 13^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2184$	$16$	$0$	$1$	$1$		$0$	$3773952$	$2.959526$	$531373116625/2058$	$0.99657$	$5.94847$	$[1, 1, 0, -42713570, 107429494866]$	$y^2+xy=x^3+x^2-42713570x+107429494866$	3.4.0.a.1, 168.8.0.?, 273.8.0.?, 312.8.0.?, 2184.16.0.?	$[ ]$
49686.cf1	49686by2	49686.cf	49686by	$2$	$3$	$ 2 \cdot 3 \cdot 7^{2} \cdot 13^{2} $	$ 2 \cdot 3 \cdot 7^{9} \cdot 13^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$168$	$16$	$0$	$6.125861177$	$1$		$0$	$290304$	$1.677050$	$531373116625/2058$	$0.99657$	$4.52528$	$[1, 1, 1, -252743, 48801059]$	$y^2+xy+y=x^3+x^2-252743x+48801059$	3.4.0.a.1, 21.8.0-3.a.1.2, 24.8.0-3.a.1.6, 168.16.0.?	$[(2861/4, 190099/4)]$
56784.r1	56784be2	56784.r	56784be	$2$	$3$	$ 2^{4} \cdot 3 \cdot 7 \cdot 13^{2} $	$ 2^{13} \cdot 3 \cdot 7^{3} \cdot 13^{4} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$168$	$16$	$0$	$0.796295839$	$1$		$12$	$145152$	$1.397243$	$531373116625/2058$	$0.99657$	$4.16336$	$[0, -1, 0, -82528, 9152896]$	$y^2=x^3-x^2-82528x+9152896$	3.4.0.a.1, 12.8.0-3.a.1.2, 168.16.0.?	$[(152, 312), (165, 26)]$
56784.x1	56784bu2	56784.x	56784bu	$2$	$3$	$ 2^{4} \cdot 3 \cdot 7 \cdot 13^{2} $	$ 2^{13} \cdot 3 \cdot 7^{3} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2184$	$16$	$0$	$4.030258543$	$1$		$2$	$1886976$	$2.679718$	$531373116625/2058$	$0.99657$	$5.56919$	$[0, -1, 0, -13947288, 20053123440]$	$y^2=x^3-x^2-13947288x+20053123440$	3.4.0.a.1, 156.8.0.?, 168.8.0.?, 2184.16.0.?	$[(2153, 112)]$
149058.ca1	149058fp2	149058.ca	149058fp	$2$	$3$	$ 2 \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} $	$ 2 \cdot 3^{7} \cdot 7^{9} \cdot 13^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$168$	$16$	$0$	$4.311714816$	$1$		$0$	$2322432$	$2.226357$	$531373116625/2058$	$0.99657$	$4.66129$	$[1, -1, 0, -2274687, -1319903285]$	$y^2+xy=x^3-x^2-2274687x-1319903285$	3.4.0.a.1, 21.8.0-3.a.1.1, 24.8.0-3.a.1.5, 168.16.0.?	$[(-21769/5, 62581/5)]$
149058.gr1	149058bj2	149058.gr	149058bj	$2$	$3$	$ 2 \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} $	$ 2 \cdot 3^{7} \cdot 7^{9} \cdot 13^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2184$	$16$	$0$	$1$	$9$	$3$	$0$	$30191616$	$3.508831$	$531373116625/2058$	$0.99657$	$5.95323$	$[1, -1, 1, -384422135, -2900980783515]$	$y^2+xy+y=x^3-x^2-384422135x-2900980783515$	3.4.0.a.1, 168.8.0.?, 273.8.0.?, 312.8.0.?, 2184.16.0.?	$[ ]$
170352.da1	170352bs2	170352.da	170352bs	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 13^{2} $	$ 2^{13} \cdot 3^{7} \cdot 7^{3} \cdot 13^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$168$	$16$	$0$	$1.785744978$	$1$		$4$	$1161216$	$1.946548$	$531373116625/2058$	$0.99657$	$4.33087$	$[0, 0, 0, -742755, -246385438]$	$y^2=x^3-742755x-246385438$	3.4.0.a.1, 12.8.0-3.a.1.1, 168.16.0.?	$[(-497, 18)]$
170352.dk1	170352bk2	170352.dk	170352bk	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 13^{2} $	$ 2^{13} \cdot 3^{7} \cdot 7^{3} \cdot 13^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2184$	$16$	$0$	$1$	$1$		$0$	$15095808$	$3.229023$	$531373116625/2058$	$0.99657$	$5.60848$	$[0, 0, 0, -125525595, -541308807286]$	$y^2=x^3-125525595x-541308807286$	3.4.0.a.1, 156.8.0.?, 168.8.0.?, 2184.16.0.?	$[ ]$
177450.bd1	177450kb2	177450.bd	177450kb	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13^{2} $	$ 2 \cdot 3 \cdot 5^{6} \cdot 7^{3} \cdot 13^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$840$	$16$	$0$	$7.256190081$	$1$		$0$	$870912$	$1.508814$	$531373116625/2058$	$0.99657$	$3.88163$	$[1, 1, 0, -128950, -17876750]$	$y^2+xy=x^3+x^2-128950x-17876750$	3.4.0.a.1, 15.8.0-3.a.1.1, 168.8.0.?, 840.16.0.?	$[(-74935/19, 667070/19)]$
177450.gu1	177450dn2	177450.gu	177450dn	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13^{2} $	$ 2 \cdot 3 \cdot 5^{6} \cdot 7^{3} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$10920$	$16$	$0$	$19.62932680$	$1$		$0$	$11321856$	$2.791290$	$531373116625/2058$	$0.99657$	$5.15494$	$[1, 1, 1, -21792638, -39166256719]$	$y^2+xy+y=x^3+x^2-21792638x-39166256719$	3.4.0.a.1, 168.8.0.?, 195.8.0.?, 10920.16.0.?	$[(-17677353725/2562, 27412000486261/2562)]$
227136.cl1	227136ik2	227136.cl	227136ik	$2$	$3$	$ 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} $	$ 2^{19} \cdot 3 \cdot 7^{3} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2184$	$16$	$0$	$33.03386730$	$1$		$0$	$15095808$	$3.026291$	$531373116625/2058$	$0.99657$	$5.28041$	$[0, -1, 0, -55789153, -160369198367]$	$y^2=x^3-x^2-55789153x-160369198367$	3.4.0.a.1, 168.8.0.?, 312.8.0.?, 546.8.0.?, 2184.16.0.?	$[(-22309826581380711/2274775, 8584778116973134976288/2274775)]$
227136.co1	227136ic2	227136.co	227136ic	$2$	$3$	$ 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} $	$ 2^{19} \cdot 3 \cdot 7^{3} \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$168$	$16$	$0$	$1$	$1$		$0$	$1161216$	$1.743816$	$531373116625/2058$	$0.99657$	$4.03259$	$[0, -1, 0, -330113, -72893055]$	$y^2=x^3-x^2-330113x-72893055$	3.4.0.a.1, 24.8.0-3.a.1.1, 42.8.0-3.a.1.2, 168.16.0.?	$[ ]$
227136.gz1	227136bg2	227136.gz	227136bg	$2$	$3$	$ 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} $	$ 2^{19} \cdot 3 \cdot 7^{3} \cdot 13^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$168$	$16$	$0$	$8.702283347$	$1$		$0$	$1161216$	$1.743816$	$531373116625/2058$	$0.99657$	$4.03259$	$[0, 1, 0, -330113, 72893055]$	$y^2=x^3+x^2-330113x+72893055$	3.4.0.a.1, 24.8.0-3.a.1.3, 84.8.0.?, 168.16.0.?	$[(119337/19, 139296/19)]$
227136.hc1	227136ba2	227136.hc	227136ba	$2$	$3$	$ 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} $	$ 2^{19} \cdot 3 \cdot 7^{3} \cdot 13^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2184$	$16$	$0$	$1$	$1$		$0$	$15095808$	$3.026291$	$531373116625/2058$	$0.99657$	$5.28041$	$[0, 1, 0, -55789153, 160369198367]$	$y^2=x^3+x^2-55789153x+160369198367$	3.4.0.a.1, 168.8.0.?, 312.8.0.?, 1092.8.0.?, 2184.16.0.?	$[ ]$
397488.hp1	397488hp2	397488.hp	397488hp	$2$	$3$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 13^{2} $	$ 2^{13} \cdot 3 \cdot 7^{9} \cdot 13^{4} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$168$	$16$	$0$	$11.19567186$	$1$		$2$	$6967296$	$2.370197$	$531373116625/2058$	$0.99657$	$4.44056$	$[0, 1, 0, -4043888, -3131355564]$	$y^2=x^3+x^2-4043888x-3131355564$	3.4.0.a.1, 24.8.0-3.a.1.8, 84.8.0.?, 168.16.0.?	$[(-10454/3, 2744/3), (10026, 981960)]$
397488.hz1	397488hz2	397488.hz	397488hz	$2$	$3$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 13^{2} $	$ 2^{13} \cdot 3 \cdot 7^{9} \cdot 13^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2184$	$16$	$0$	$1$	$9$	$3$	$0$	$90574848$	$3.652672$	$531373116625/2058$	$0.99657$	$5.63421$	$[0, 1, 0, -683417128, -6876854505676]$	$y^2=x^3+x^2-683417128x-6876854505676$	3.4.0.a.1, 168.8.0.?, 312.8.0.?, 1092.8.0.?, 2184.16.0.?	$[ ]$

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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.

Refine search