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

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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
20328.y1	20328u2	20328.y	20328u	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} $	$ 2^{11} \cdot 3^{2} \cdot 7^{2} \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$10.94508902$	$1$	$1$	$84480$	$1.660276$	$2450086/441$	$0.85310$	$4.42726$	$[0, 1, 0, -47472, -3320352]$	$y^2=x^3+x^2-47472x-3320352$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[(-106453/29, 20060586/29)]$
20328.bc1	20328g2	20328.bc	20328g	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} $	$ 2^{11} \cdot 3^{2} \cdot 7^{2} \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$2.507640288$	$1$	$3$	$7680$	$0.461328$	$2450086/441$	$0.85310$	$2.97688$	$[0, 1, 0, -392, 2352]$	$y^2=x^3+x^2-392x+2352$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[(-21, 42)]$
40656.bg1	40656b2	40656.bg	40656b	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7 \cdot 11^{2} $	$ 2^{11} \cdot 3^{2} \cdot 7^{2} \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1.160453260$	$1$	$7$	$15360$	$0.461328$	$2450086/441$	$0.85310$	$2.78246$	$[0, -1, 0, -392, -2352]$	$y^2=x^3-x^2-392x-2352$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[(26, 66)]$
40656.bl1	40656o2	40656.bl	40656o	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7 \cdot 11^{2} $	$ 2^{11} \cdot 3^{2} \cdot 7^{2} \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1$	$1$	$1$	$168960$	$1.660276$	$2450086/441$	$0.85310$	$4.13811$	$[0, -1, 0, -47472, 3320352]$	$y^2=x^3-x^2-47472x+3320352$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[]$
60984.j1	60984o2	60984.j	60984o	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ 2^{11} \cdot 3^{8} \cdot 7^{2} \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1$	$1$	$1$	$675840$	$2.209583$	$2450086/441$	$0.85310$	$4.58407$	$[0, 0, 0, -427251, 89222254]$	$y^2=x^3-427251x+89222254$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[]$
60984.q1	60984cb2	60984.q	60984cb	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ 2^{11} \cdot 3^{8} \cdot 7^{2} \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1$	$1$	$1$	$61440$	$1.010633$	$2450086/441$	$0.85310$	$3.27831$	$[0, 0, 0, -3531, -67034]$	$y^2=x^3-3531x-67034$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[]$
121968.bb1	121968ba2	121968.bb	121968ba	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ 2^{11} \cdot 3^{8} \cdot 7^{2} \cdot 11^{3} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$0.772605092$	$1$	$27$	$122880$	$1.010633$	$2450086/441$	$0.85310$	$3.08428$	$[0, 0, 0, -3531, 67034]$	$y^2=x^3-3531x+67034$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[(1, 252), (55, 198)]$
121968.bs1	121968bs2	121968.bs	121968bs	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ 2^{11} \cdot 3^{8} \cdot 7^{2} \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$3.710993620$	$1$	$3$	$1351680$	$2.209583$	$2450086/441$	$0.85310$	$4.31276$	$[0, 0, 0, -427251, -89222254]$	$y^2=x^3-427251x-89222254$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[(-494, 1134)]$
142296.i1	142296bb2	142296.i	142296bb	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 11^{2} $	$ 2^{11} \cdot 3^{2} \cdot 7^{8} \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$5.796072232$	$1$	$3$	$4055040$	$2.633232$	$2450086/441$	$0.85310$	$4.68518$	$[0, -1, 0, -2326144, 1134228460]$	$y^2=x^3-x^2-2326144x+1134228460$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[(-1227, 46256)]$
142296.k1	142296cz2	142296.k	142296cz	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 11^{2} $	$ 2^{11} \cdot 3^{2} \cdot 7^{8} \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1$	$1$	$1$	$368640$	$1.434282$	$2450086/441$	$0.85310$	$3.47266$	$[0, -1, 0, -19224, -845172]$	$y^2=x^3-x^2-19224x-845172$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[]$
162624.r1	162624hm2	162624.r	162624hm	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7 \cdot 11^{2} $	$ 2^{17} \cdot 3^{2} \cdot 7^{2} \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$4.166589876$	$1$	$5$	$1351680$	$2.006851$	$2450086/441$	$0.85310$	$4.00662$	$[0, -1, 0, -189889, -26372927]$	$y^2=x^3-x^2-189889x-26372927$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[(-189, 1652)]$
162624.bf1	162624hi2	162624.bf	162624hi	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7 \cdot 11^{2} $	$ 2^{17} \cdot 3^{2} \cdot 7^{2} \cdot 11^{3} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1.205128932$	$1$	$19$	$122880$	$0.807901$	$2450086/441$	$0.85310$	$2.80759$	$[0, -1, 0, -1569, 20385]$	$y^2=x^3-x^2-1569x+20385$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[(-7, 176), (-39, 144)]$
162624.fl1	162624o2	162624.fl	162624o	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7 \cdot 11^{2} $	$ 2^{17} \cdot 3^{2} \cdot 7^{2} \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$2.496155865$	$1$	$5$	$122880$	$0.807901$	$2450086/441$	$0.85310$	$2.80759$	$[0, 1, 0, -1569, -20385]$	$y^2=x^3+x^2-1569x-20385$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[(-22, 63)]$
162624.fs1	162624i2	162624.fs	162624i	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7 \cdot 11^{2} $	$ 2^{17} \cdot 3^{2} \cdot 7^{2} \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1$	$1$	$1$	$1351680$	$2.006851$	$2450086/441$	$0.85310$	$4.00662$	$[0, 1, 0, -189889, 26372927]$	$y^2=x^3+x^2-189889x+26372927$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[]$
284592.gs1	284592gs2	284592.gs	284592gs	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 11^{2} $	$ 2^{11} \cdot 3^{2} \cdot 7^{8} \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$3.361224572$	$1$	$5$	$8110080$	$2.633232$	$2450086/441$	$0.85310$	$4.42659$	$[0, 1, 0, -2326144, -1134228460]$	$y^2=x^3+x^2-2326144x-1134228460$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[(-586, 5292)]$
284592.hd1	284592hd2	284592.hd	284592hd	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 11^{2} $	$ 2^{11} \cdot 3^{2} \cdot 7^{8} \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$2.077958978$	$1$	$5$	$737280$	$1.434282$	$2450086/441$	$0.85310$	$3.28100$	$[0, 1, 0, -19224, 845172]$	$y^2=x^3+x^2-19224x+845172$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[(44, 294)]$
426888.gd1	426888gd2	426888.gd	426888gd	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} $	$ 2^{11} \cdot 3^{8} \cdot 7^{8} \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$18.87337450$	$1$	$1$	$32440320$	$3.182537$	$2450086/441$	$0.85310$	$4.79660$	$[0, 0, 0, -20935299, -30603233122]$	$y^2=x^3-20935299x-30603233122$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[(-4947915959/1208, 65953478763333/1208)]$
426888.gl1	426888gl2	426888.gl	426888gl	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} $	$ 2^{11} \cdot 3^{8} \cdot 7^{8} \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1$	$1$	$1$	$2949120$	$1.983589$	$2450086/441$	$0.85310$	$3.68683$	$[0, 0, 0, -173019, 22992662]$	$y^2=x^3-173019x+22992662$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[]$
487872.mi1	487872mi2	487872.mi	487872mi	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ 2^{17} \cdot 3^{8} \cdot 7^{2} \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1$	$1$	$1$	$10813440$	$2.556156$	$2450086/441$	$0.85310$	$4.17382$	$[0, 0, 0, -1709004, 713778032]$	$y^2=x^3-1709004x+713778032$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[]$
487872.mt1	487872mt2	487872.mt	487872mt	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ 2^{17} \cdot 3^{8} \cdot 7^{2} \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1.097467510$	$1$	$7$	$983040$	$1.357208$	$2450086/441$	$0.85310$	$3.07536$	$[0, 0, 0, -14124, 536272]$	$y^2=x^3-14124x+536272$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[(26, 432)]$
487872.nq1	487872nq2	487872.nq	487872nq	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ 2^{17} \cdot 3^{8} \cdot 7^{2} \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1$	$1$	$1$	$10813440$	$2.556156$	$2450086/441$	$0.85310$	$4.17382$	$[0, 0, 0, -1709004, -713778032]$	$y^2=x^3-1709004x-713778032$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[]$
487872.ob1	487872ob2	487872.ob	487872ob	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ 2^{17} \cdot 3^{8} \cdot 7^{2} \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$3.319874706$	$1$	$3$	$983040$	$1.357208$	$2450086/441$	$0.85310$	$3.07536$	$[0, 0, 0, -14124, -536272]$	$y^2=x^3-14124x-536272$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 924.6.0.?, 1848.12.0.?	$[(484, 10296)]$

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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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