LMFDB - Elliptic curves over $\Q$ of conductor 52094

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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

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

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Results (26 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
52094.a1	52094b2	52094.a	52094b	$2$	$3$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2 \cdot 7^{3} \cdot 61^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$10248$	$16$	$0$	$4.330409052$	$1$		$0$	$23760$	$0.266969$	$7309212577/686$	$0.89401$	$2.84824$	$[1, 0, 1, -627, -6088]$	$y^2+xy+y=x^3-627x-6088$	3.4.0.a.1, 56.2.0.a.1, 168.8.0.?, 183.8.0.?, 10248.16.0.?	$[(-366/5, 863/5)]$
52094.a2	52094b1	52094.a	52094b	$2$	$3$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2^{3} \cdot 7 \cdot 61^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$10248$	$16$	$0$	$1.443469684$	$1$		$2$	$7920$	$-0.282338$	$134017/56$	$0.75310$	$1.84401$	$[1, 0, 1, -17, 12]$	$y^2+xy+y=x^3-17x+12$	3.4.0.a.1, 56.2.0.a.1, 168.8.0.?, 183.8.0.?, 10248.16.0.?	$[(0, 3)]$
52094.b1	52094a1	52094.b	52094a	$1$	$1$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2^{6} \cdot 7^{7} \cdot 61^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1708$	$2$	$0$	$1.164495111$	$1$		$4$	$1249920$	$2.574596$	$7026036894577/3215111872$	$0.93264$	$4.99465$	$[1, 1, 0, -1484756, 317934736]$	$y^2+xy=x^3+x^2-1484756x+317934736$	1708.2.0.?	$[(1184, 14292)]$
52094.c1	52094e1	52094.c	52094e	$1$	$1$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2^{8} \cdot 7 \cdot 61^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1708$	$2$	$0$	$1$	$1$		$0$	$238080$	$1.717684$	$244140625/109312$	$1.05125$	$4.04929$	$[1, 1, 0, -48450, 1932532]$	$y^2+xy=x^3+x^2-48450x+1932532$	1708.2.0.?	$[]$
52094.d1	52094f1	52094.d	52094f	$1$	$1$	$ 2 \cdot 7 \cdot 61^{2} $	$ - 2^{3} \cdot 7 \cdot 61^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$56$	$2$	$0$	$1$	$1$		$0$	$20880$	$0.387138$	$-3721/56$	$0.84643$	$2.57451$	$[1, 1, 0, -77, 1333]$	$y^2+xy=x^3+x^2-77x+1333$	56.2.0.b.1	$[]$
52094.e1	52094d2	52094.e	52094d	$2$	$3$	$ 2 \cdot 7 \cdot 61^{2} $	$ - 2^{21} \cdot 7 \cdot 61^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$168$	$16$	$0$	$1$	$25$	$5$	$0$	$4611600$	$2.870090$	$-237419290537/14680064$	$1.01294$	$5.44910$	$[1, 0, 1, -7438357, -8215610528]$	$y^2+xy+y=x^3-7438357x-8215610528$	3.8.0-3.a.1.1, 56.2.0.b.1, 168.16.0.?	$[]$
52094.e2	52094d1	52094.e	52094d	$2$	$3$	$ 2 \cdot 7 \cdot 61^{2} $	$ - 2^{7} \cdot 7^{3} \cdot 61^{8} $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$168$	$16$	$0$	$1$	$25$	$5$	$2$	$1537200$	$2.320786$	$74727623/43904$	$0.93077$	$4.69729$	$[1, 0, 1, 505978, -17056808]$	$y^2+xy+y=x^3+505978x-17056808$	3.8.0-3.a.1.2, 56.2.0.b.1, 168.16.0.?	$[]$
52094.f1	52094c2	52094.f	52094c	$2$	$5$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2^{10} \cdot 7^{5} \cdot 61^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$8540$	$48$	$1$	$1$	$1$		$0$	$216000$	$1.223417$	$1298239519429/17210368$	$0.96097$	$3.70365$	$[1, 0, 1, -13864, 619894]$	$y^2+xy+y=x^3-13864x+619894$	5.6.0.a.1, 140.12.0.?, 305.24.0.?, 1708.2.0.?, 8540.48.1.?	$[]$
52094.f2	52094c1	52094.f	52094c	$2$	$5$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2^{2} \cdot 7 \cdot 61^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$8540$	$48$	$1$	$1$	$1$		$0$	$43200$	$0.418698$	$1221611509/28$	$0.96779$	$3.06203$	$[1, 0, 1, -1359, -19386]$	$y^2+xy+y=x^3-1359x-19386$	5.6.0.a.1, 140.12.0.?, 305.24.0.?, 1708.2.0.?, 8540.48.1.?	$[]$
52094.g1	52094j6	52094.g	52094j	$6$	$18$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2^{9} \cdot 7^{2} \cdot 61^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.6, 9.12.0.1	2B, 3B	$30744$	$864$	$21$	$1$	$1$		$0$	$1360800$	$2.468536$	$2251439055699625/25088$	$1.06489$	$5.52589$	$[1, 0, 0, -10160268, -12466236272]$	$y^2+xy=x^3-10160268x-12466236272$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$	$[]$
52094.g2	52094j5	52094.g	52094j	$6$	$18$	$ 2 \cdot 7 \cdot 61^{2} $	$ - 2^{18} \cdot 7 \cdot 61^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.1, 9.12.0.1	2B, 3B	$30744$	$864$	$21$	$1$	$1$		$1$	$680400$	$2.121964$	$-548347731625/1835008$	$1.02933$	$4.76035$	$[1, 0, 0, -634508, -195152240]$	$y^2+xy=x^3-634508x-195152240$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$	$[]$
52094.g3	52094j4	52094.g	52094j	$6$	$18$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2^{3} \cdot 7^{6} \cdot 61^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.6, 3.12.0.1	2B, 3Cs	$30744$	$864$	$21$	$1$	$1$		$0$	$453600$	$1.919231$	$4956477625/941192$	$1.00821$	$4.32649$	$[1, 0, 0, -132173, -15171191]$	$y^2+xy=x^3-132173x-15171191$	2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.b.1, 24.72.1.h.1, $\ldots$	$[]$
52094.g4	52094j2	52094.g	52094j	$6$	$18$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2 \cdot 7^{2} \cdot 61^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.6, 9.12.0.1	2B, 3B	$30744$	$864$	$21$	$1$	$1$		$0$	$151200$	$1.369926$	$128787625/98$	$0.96763$	$3.99040$	$[1, 0, 0, -39148, 2976126]$	$y^2+xy=x^3-39148x+2976126$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$	$[]$
52094.g5	52094j1	52094.g	52094j	$6$	$18$	$ 2 \cdot 7 \cdot 61^{2} $	$ - 2^{2} \cdot 7 \cdot 61^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.1, 9.12.0.1	2B, 3B	$30744$	$864$	$21$	$1$	$1$		$1$	$75600$	$1.023352$	$-15625/28$	$1.01712$	$3.29000$	$[1, 0, 0, -1938, 66304]$	$y^2+xy=x^3-1938x+66304$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$	$[]$
52094.g6	52094j3	52094.g	52094j	$6$	$18$	$ 2 \cdot 7 \cdot 61^{2} $	$ - 2^{6} \cdot 7^{3} \cdot 61^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.1, 3.12.0.1	2B, 3Cs	$30744$	$864$	$21$	$1$	$1$		$1$	$226800$	$1.572659$	$9938375/21952$	$0.98695$	$3.84988$	$[1, 0, 0, 16667, -1388607]$	$y^2+xy=x^3+16667x-1388607$	2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.c.1, 14.6.0.b.1, $\ldots$	$[]$
52094.h1	52094l2	52094.h	52094l	$2$	$3$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2 \cdot 7^{3} \cdot 61^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$168$	$16$	$0$	$7.654261677$	$1$		$0$	$1449360$	$2.322407$	$7309212577/686$	$0.89401$	$5.11927$	$[1, 0, 0, -2331284, -1370147294]$	$y^2+xy=x^3-2331284x-1370147294$	3.8.0-3.a.1.1, 56.2.0.a.1, 168.16.0.?	$[(-8877899/100, 543733101/100)]$
52094.h2	52094l1	52094.h	52094l	$2$	$3$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2^{3} \cdot 7 \cdot 61^{8} $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$168$	$16$	$0$	$22.96278503$	$1$		$2$	$483120$	$1.773100$	$134017/56$	$0.75310$	$4.11505$	$[1, 0, 0, -61474, 3087756]$	$y^2+xy=x^3-61474x+3087756$	3.8.0-3.a.1.2, 56.2.0.a.1, 168.16.0.?	$[(-6196130611/4900, 172243288834987/4900)]$
52094.i1	52094i1	52094.i	52094i	$1$	$1$	$ 2 \cdot 7 \cdot 61^{2} $	$ - 2^{3} \cdot 7 \cdot 61^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$56$	$2$	$0$	$1$	$1$		$0$	$1273680$	$2.442574$	$-3721/56$	$0.84643$	$4.84555$	$[1, 1, 1, -288455, 309760629]$	$y^2+xy+y=x^3+x^2-288455x+309760629$	56.2.0.b.1	$[]$
52094.j1	52094k1	52094.j	52094k	$1$	$1$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2^{10} \cdot 7^{3} \cdot 61^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1708$	$2$	$0$	$0.269186288$	$1$		$6$	$892800$	$2.413319$	$41540367914137/21425152$	$0.92284$	$5.15827$	$[1, 0, 0, -2684779, 1692231985]$	$y^2+xy=x^3-2684779x+1692231985$	1708.2.0.?	$[(-1398, 52793)]$
52094.k1	52094g3	52094.k	52094g	$3$	$9$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2^{36} \cdot 7 \cdot 61^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$15372$	$144$	$3$	$1$	$1$		$0$	$9642240$	$3.540226$	$19604918227371765625/29343216566272$	$1.02695$	$6.36118$	$[1, 0, 0, -209029113, -1161722623495]$	$y^2+xy=x^3-209029113x-1161722623495$	3.4.0.a.1, 9.12.0.a.1, 84.8.0.?, 183.8.0.?, 252.24.0.?, $\ldots$	$[]$
52094.k2	52094g2	52094.k	52094g	$3$	$9$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2^{12} \cdot 7^{3} \cdot 61^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.12.0.1	3Cs	$15372$	$144$	$3$	$1$	$1$		$0$	$3214080$	$2.990921$	$2429070588015625/318891962368$	$0.99422$	$5.53288$	$[1, 0, 0, -10420738, 11383959748]$	$y^2+xy=x^3-10420738x+11383959748$	3.12.0.a.1, 84.24.0.?, 183.24.0.?, 1708.2.0.?, 3843.72.0.?, $\ldots$	$[]$
52094.k3	52094g1	52094.k	52094g	$3$	$9$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2^{4} \cdot 7 \cdot 61^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$15372$	$144$	$3$	$1$	$1$		$0$	$1071360$	$2.441612$	$2190162605289625/6832$	$0.94739$	$5.52335$	$[1, 0, 0, -10067243, 12293747969]$	$y^2+xy=x^3-10067243x+12293747969$	3.4.0.a.1, 9.12.0.a.1, 84.8.0.?, 183.8.0.?, 252.24.0.?, $\ldots$	$[]$
52094.l1	52094h2	52094.l	52094h	$2$	$3$	$ 2 \cdot 7 \cdot 61^{2} $	$ - 2^{21} \cdot 7 \cdot 61^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$10248$	$16$	$0$	$1$	$1$		$0$	$75600$	$0.814654$	$-237419290537/14680064$	$1.01294$	$3.17807$	$[1, 0, 0, -1999, -36359]$	$y^2+xy=x^3-1999x-36359$	3.4.0.a.1, 56.2.0.b.1, 168.8.0.?, 183.8.0.?, 10248.16.0.?	$[]$
52094.l2	52094h1	52094.l	52094h	$2$	$3$	$ 2 \cdot 7 \cdot 61^{2} $	$ - 2^{7} \cdot 7^{3} \cdot 61^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$10248$	$16$	$0$	$1$	$1$		$0$	$25200$	$0.265348$	$74727623/43904$	$0.93077$	$2.42626$	$[1, 0, 0, 136, -64]$	$y^2+xy=x^3+136x-64$	3.4.0.a.1, 56.2.0.b.1, 168.8.0.?, 183.8.0.?, 10248.16.0.?	$[]$
52094.m1	52094m2	52094.m	52094m	$2$	$5$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2^{10} \cdot 7^{5} \cdot 61^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$8540$	$48$	$1$	$1$	$1$		$0$	$13176000$	$3.278854$	$1298239519429/17210368$	$0.96097$	$5.97469$	$[1, 0, 0, -51586161, 140962147433]$	$y^2+xy=x^3-51586161x+140962147433$	5.6.0.a.1, 140.12.0.?, 305.24.0.?, 1708.2.0.?, 8540.48.1.?	$[]$
52094.m2	52094m1	52094.m	52094m	$2$	$5$	$ 2 \cdot 7 \cdot 61^{2} $	$ 2^{2} \cdot 7 \cdot 61^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$8540$	$48$	$1$	$1$	$25$	$5$	$0$	$2635200$	$2.474136$	$1221611509/28$	$0.96779$	$5.33306$	$[1, 0, 0, -5055056, -4374921772]$	$y^2+xy=x^3-5055056x-4374921772$	5.6.0.a.1, 140.12.0.?, 305.24.0.?, 1708.2.0.?, 8540.48.1.?	$[]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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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