LMFDB - Elliptic curves over $\Q$ of conductor 29008

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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 (23 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
29008.a1	29008k1	29008.a	29008k	$1$	$1$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ 2^{12} \cdot 7^{6} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$74$	$2$	$0$	$3.824624232$	$1$		$2$	$30240$	$0.669560$	$110592/37$	$0.76978$	$3.07599$	$[0, 0, 0, -784, 5488]$	$y^2=x^3-784x+5488$	74.2.0.?	$[(-31, 1)]$
29008.b1	29008o1	29008.b	29008o	$1$	$1$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 7^{3} \cdot 37 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$518$	$2$	$0$	$0.519078696$	$1$		$14$	$3840$	$-0.047355$	$-65536/37$	$0.74764$	$2.25337$	$[0, 1, 0, -37, 111]$	$y^2=x^3+x^2-37x+111$	518.2.0.?	$[(-5, 14), (2, 7)]$
29008.c1	29008h2	29008.c	29008h	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ 2^{11} \cdot 7^{3} \cdot 37 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$4$	$2$	$1$	$28672$	$0.820271$	$212319530750/37$	$0.92212$	$3.84841$	$[0, 1, 0, -11048, -450668]$	$y^2=x^3+x^2-11048x-450668$	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
29008.c2	29008h1	29008.c	29008h	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ - 2^{10} \cdot 7^{3} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$14336$	$0.473697$	$-102689500/1369$	$0.82913$	$3.04021$	$[0, 1, 0, -688, -7260]$	$y^2=x^3+x^2-688x-7260$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[ ]$
29008.d1	29008i1	29008.d	29008i	$1$	$1$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ 2^{8} \cdot 7^{6} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$74$	$2$	$0$	$2.724622073$	$1$		$2$	$10560$	$0.616788$	$16000000/37$	$0.93985$	$3.29028$	$[0, -1, 0, -1633, 25901]$	$y^2=x^3-x^2-1633x+25901$	74.2.0.?	$[(20, 29)]$
29008.e1	29008e1	29008.e	29008e	$1$	$1$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ 2^{8} \cdot 7^{6} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$74$	$2$	$0$	$1$	$1$		$0$	$12096$	$0.470715$	$351232/37$	$0.74527$	$2.91863$	$[0, -1, 0, -457, 3557]$	$y^2=x^3-x^2-457x+3557$	74.2.0.?	$[ ]$
29008.f1	29008m1	29008.f	29008m	$1$	$1$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ 2^{8} \cdot 7^{6} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$74$	$2$	$0$	$1$	$1$		$0$	$15840$	$0.425990$	$65536/37$	$0.98850$	$2.75524$	$[0, -1, 0, -261, -167]$	$y^2=x^3-x^2-261x-167$	74.2.0.?	$[ ]$
29008.g1	29008j2	29008.g	29008j	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ 2^{12} \cdot 7^{12} \cdot 37 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$2.231009676$	$1$		$5$	$221184$	$1.781385$	$760798453689/4353013$	$0.97619$	$4.60821$	$[0, 0, 0, -149107, -22051470]$	$y^2=x^3-149107x-22051470$	2.3.0.a.1, 28.6.0.c.1, 74.6.0.?, 1036.12.0.?	$[(-217, 294)]$
29008.g2	29008j1	29008.g	29008j	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ - 2^{12} \cdot 7^{9} \cdot 37^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1.115504838$	$1$		$7$	$110592$	$1.434813$	$-15438249/469567$	$0.97720$	$3.94405$	$[0, 0, 0, -4067, -730590]$	$y^2=x^3-4067x-730590$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[(119, 686)]$
29008.h1	29008c1	29008.h	29008c	$1$	$1$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 7^{7} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$518$	$2$	$0$	$1$	$1$		$0$	$18432$	$0.579333$	$27648/259$	$0.75618$	$2.93601$	$[0, 0, 0, 196, -4116]$	$y^2=x^3+196x-4116$	518.2.0.?	$[ ]$
29008.i1	29008a1	29008.i	29008a	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ 2^{4} \cdot 7^{8} \cdot 37 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$1$		$1$	$10752$	$0.538042$	$6912000/1813$	$0.92588$	$2.93877$	$[0, 0, 0, -490, 3087]$	$y^2=x^3-490x+3087$	2.3.0.a.1, 28.6.0.c.1, 74.6.0.?, 1036.12.0.?	$[ ]$
29008.i2	29008a2	29008.i	29008a	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 7^{7} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$1$		$1$	$21504$	$0.884616$	$6750000/9583$	$0.85629$	$3.24267$	$[0, 0, 0, 1225, 19894]$	$y^2=x^3+1225x+19894$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[ ]$
29008.j1	29008b1	29008.j	29008b	$1$	$1$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 7^{13} \cdot 37^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$518$	$2$	$0$	$1$	$1$		$0$	$387072$	$2.346493$	$-15283295882302464/41714923579$	$1.00656$	$5.30308$	$[0, 0, 0, -1608572, 787101308]$	$y^2=x^3-1608572x+787101308$	518.2.0.?	$[ ]$
29008.k1	29008d1	29008.k	29008d	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ 2^{4} \cdot 7^{8} \cdot 37^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$25$	$5$	$1$	$235008$	$1.880695$	$33256413948450816/2481997$	$1.11932$	$5.10846$	$[0, 0, 0, -827218, -289586325]$	$y^2=x^3-827218x-289586325$	2.3.0.a.1, 28.6.0.c.1, 74.6.0.?, 1036.12.0.?	$[ ]$
29008.k2	29008d2	29008.k	29008d	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 7^{7} \cdot 37^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$25$	$5$	$1$	$470016$	$2.227268$	$-2065624967846736/17960084863$	$1.06882$	$5.10930$	$[0, 0, 0, -825503, -290846850]$	$y^2=x^3-825503x-290846850$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[ ]$
29008.l1	29008l3	29008.l	29008l	$3$	$9$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ 2^{12} \cdot 7^{6} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	27.36.0.1	3B	$27972$	$1296$	$43$	$1$	$9$	$3$	$0$	$163296$	$1.888184$	$727057727488000/37$	$1.08598$	$5.27606$	$[0, 1, 0, -1468693, -685575101]$	$y^2=x^3+x^2-1468693x-685575101$	3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 74.2.0.?, 84.8.0.?, $\ldots$	$[ ]$
29008.l2	29008l2	29008.l	29008l	$3$	$9$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ 2^{12} \cdot 7^{6} \cdot 37^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.36.0.2	3Cs	$27972$	$1296$	$43$	$1$	$1$		$0$	$54432$	$1.338877$	$1404928000/50653$	$0.97274$	$3.99564$	$[0, 1, 0, -18293, -928285]$	$y^2=x^3+x^2-18293x-928285$	3.12.0.a.1, 9.36.0.b.1, 74.2.0.?, 84.24.0.?, 222.24.1.?, $\ldots$	$[ ]$
29008.l3	29008l1	29008.l	29008l	$3$	$9$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ 2^{12} \cdot 7^{6} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	27.36.0.1	3B	$27972$	$1296$	$43$	$1$	$1$		$0$	$18144$	$0.789572$	$4096000/37$	$0.88268$	$3.42751$	$[0, 1, 0, -2613, 50147]$	$y^2=x^3+x^2-2613x+50147$	3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 74.2.0.?, 84.8.0.?, $\ldots$	$[ ]$
29008.m1	29008f2	29008.m	29008f	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ 2^{11} \cdot 7^{9} \cdot 37 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$4$	$2$	$1$	$200704$	$1.793224$	$212319530750/37$	$0.92212$	$4.98468$	$[0, -1, 0, -541368, 153496400]$	$y^2=x^3-x^2-541368x+153496400$	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
29008.m2	29008f1	29008.m	29008f	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ - 2^{10} \cdot 7^{9} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$100352$	$1.446651$	$-102689500/1369$	$0.82913$	$4.17648$	$[0, -1, 0, -33728, 2422736]$	$y^2=x^3-x^2-33728x+2422736$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[ ]$
29008.n1	29008g2	29008.n	29008g	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ 2^{11} \cdot 7^{12} \cdot 37 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$4$	$2$	$1$	$165888$	$1.664446$	$169556172914/4353013$	$0.88931$	$4.39466$	$[0, -1, 0, -71752, -7207920]$	$y^2=x^3-x^2-71752x-7207920$	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
29008.n2	29008g1	29008.n	29008g	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ - 2^{10} \cdot 7^{9} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$4$	$2$	$1$	$82944$	$1.317873$	$415292/469567$	$0.92128$	$3.80725$	$[0, -1, 0, 768, -362032]$	$y^2=x^3-x^2+768x-362032$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[ ]$
29008.o1	29008n1	29008.o	29008n	$1$	$1$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 7^{9} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$518$	$2$	$0$	$1$	$4$	$2$	$0$	$26880$	$0.925600$	$-65536/37$	$0.74764$	$3.38963$	$[0, -1, 0, -1829, -41719]$	$y^2=x^3-x^2-1829x-41719$	518.2.0.?	$[ ]$

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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.

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