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 (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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
13860.n2	13860d2	13860.n	13860d	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$5376$	$0.248410$	$2963088/21175$	$0.80341$	$2.74431$	$[0, 0, 0, 57, 558]$	$y^2=x^3+57x+558$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
13860.u2	13860g2	13860.u	13860g	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$16128$	$0.797715$	$2963088/21175$	$0.80341$	$3.43550$	$[0, 0, 0, 513, -15066]$	$y^2=x^3+513x-15066$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
55440.z2	55440bx2	55440.z	55440bx	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$21504$	$0.248410$	$2963088/21175$	$0.80341$	$2.39602$	$[0, 0, 0, 57, -558]$	$y^2=x^3+57x-558$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
55440.dt2	55440ck2	55440.dt	55440ck	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$64512$	$0.797715$	$2963088/21175$	$0.80341$	$2.99948$	$[0, 0, 0, 513, 15066]$	$y^2=x^3+513x+15066$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
69300.a2	69300d2	69300.a	69300d	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{8} \cdot 7 \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$387072$	$1.602434$	$2963088/21175$	$0.80341$	$3.80580$	$[0, 0, 0, 12825, -1883250]$	$y^2=x^3+12825x-1883250$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
69300.s2	69300h2	69300.s	69300h	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{8} \cdot 7 \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$0.837386050$	$1$	$7$	$129024$	$1.053129$	$2963088/21175$	$0.80341$	$3.21441$	$[0, 0, 0, 1425, 69750]$	$y^2=x^3+1425x+69750$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(-5, 250)]$
97020.a2	97020h2	97020.a	97020h	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{2} \cdot 7^{7} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$0.681275744$	$1$	$9$	$774144$	$1.770670$	$2963088/21175$	$0.80341$	$3.87009$	$[0, 0, 0, 25137, 5167638]$	$y^2=x^3+25137x+5167638$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(63, 2646)]$
97020.cf2	97020ba2	97020.cf	97020ba	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{2} \cdot 7^{7} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$2.136397796$	$1$	$5$	$258048$	$1.221365$	$2963088/21175$	$0.80341$	$3.29604$	$[0, 0, 0, 2793, -191394]$	$y^2=x^3+2793x-191394$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(126, 1470)]$
152460.a2	152460bw2	152460.a	152460bw	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{8} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1.008164200$	$1$	$9$	$645120$	$1.447357$	$2963088/21175$	$0.80341$	$3.39844$	$[0, 0, 0, 6897, -742698]$	$y^2=x^3+6897x-742698$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(231, 3630)]$
152460.z2	152460bk2	152460.z	152460bk	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{8} \cdot 3^{9} \cdot 5^{2} \cdot 7 \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$1935360$	$1.996664$	$2963088/21175$	$0.80341$	$3.95076$	$[0, 0, 0, 62073, 20052846]$	$y^2=x^3+62073x+20052846$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
221760.b2	221760hg2	221760.b	221760hg	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{14} \cdot 3^{9} \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$516096$	$1.144289$	$2963088/21175$	$0.80341$	$2.99954$	$[0, 0, 0, 2052, 120528]$	$y^2=x^3+2052x+120528$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
221760.ex2	221760nf2	221760.ex	221760nf	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{14} \cdot 3^{9} \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1.983124488$	$1$	$5$	$516096$	$1.144289$	$2963088/21175$	$0.80341$	$2.99954$	$[0, 0, 0, 2052, -120528]$	$y^2=x^3+2052x-120528$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(58, 440)]$
221760.if2	221760gb2	221760.if	221760gb	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{14} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$172032$	$0.594983$	$2963088/21175$	$0.80341$	$2.46404$	$[0, 0, 0, 228, -4464]$	$y^2=x^3+228x-4464$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
221760.km2	221760mo2	221760.km	221760mo	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{14} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$0.811164975$	$1$	$9$	$172032$	$0.594983$	$2963088/21175$	$0.80341$	$2.46404$	$[0, 0, 0, 228, 4464]$	$y^2=x^3+228x+4464$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(10, 88)]$
277200.gw2	277200gw2	277200.gw	277200gw	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{8} \cdot 7 \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$3.214838755$	$1$	$3$	$516096$	$1.053129$	$2963088/21175$	$0.80341$	$2.85885$	$[0, 0, 0, 1425, -69750]$	$y^2=x^3+1425x-69750$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(690, 18150)]$
277200.ky2	277200ky2	277200.ky	277200ky	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{8} \cdot 7 \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$1548288$	$1.602434$	$2963088/21175$	$0.80341$	$3.38481$	$[0, 0, 0, 12825, 1883250]$	$y^2=x^3+12825x+1883250$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
388080.ej2	388080ej2	388080.ej	388080ej	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{2} \cdot 7^{7} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$3096576$	$1.770670$	$2963088/21175$	$0.80341$	$3.45319$	$[0, 0, 0, 25137, -5167638]$	$y^2=x^3+25137x-5167638$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
388080.hq2	388080hq2	388080.hq	388080hq	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{2} \cdot 7^{7} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$1032192$	$1.221365$	$2963088/21175$	$0.80341$	$2.94098$	$[0, 0, 0, 2793, 191394]$	$y^2=x^3+2793x+191394$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
485100.dl2	485100dl2	485100.dl	485100dl	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{8} \cdot 7^{7} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$6.298401712$	$1$	$1$	$18579456$	$2.575390$	$2963088/21175$	$0.80341$	$4.13193$	$[0, 0, 0, 628425, 645954750]$	$y^2=x^3+628425x+645954750$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(1705/2, 251875/2)]$
485100.ir2	485100ir2	485100.ir	485100ir	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{8} \cdot 7^{7} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$6193152$	$2.026085$	$2963088/21175$	$0.80341$	$3.62844$	$[0, 0, 0, 69825, -23924250]$	$y^2=x^3+69825x-23924250$	2.3.0.a.1, 84.6.0.?, 660.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$

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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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