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 (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	Manin constant
2220.c2	2220c2	2220.c	2220c	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5 \cdot 37 $	$ - 2^{8} \cdot 3 \cdot 5^{15} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$1110$	$16$	$0$	$1$	$9$	$3$	$0$	$9720$	$1.550894$	$1736064508952576/3387451171875$	$1.04003$	$5.38582$	$[0, 1, 0, 15899, -1182985]$	$y^2=x^3+x^2+15899x-1182985$	3.8.0-3.a.1.1, 1110.16.0.?	$[ ]$	$1$
6660.e2	6660f2	6660.e	6660f	$2$	$3$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 37 $	$ - 2^{8} \cdot 3^{7} \cdot 5^{15} \cdot 37 $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$1110$	$16$	$0$	$1.149121569$	$1$		$10$	$77760$	$2.100201$	$1736064508952576/3387451171875$	$1.04003$	$5.46247$	$[0, 0, 0, 143088, 32083684]$	$y^2=x^3+143088x+32083684$	3.8.0-3.a.1.2, 1110.16.0.?	$[(-52, 4950)]$	$1$
8880.c2	8880p2	8880.c	8880p	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5 \cdot 37 $	$ - 2^{8} \cdot 3 \cdot 5^{15} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2220$	$16$	$0$	$4.447045485$	$1$		$2$	$38880$	$1.550894$	$1736064508952576/3387451171875$	$1.04003$	$4.56459$	$[0, -1, 0, 15899, 1182985]$	$y^2=x^3-x^2+15899x+1182985$	3.4.0.a.1, 12.8.0-3.a.1.2, 1110.8.0.?, 2220.16.0.?	$[(-15, 970)]$	$1$
11100.b2	11100b2	11100.b	11100b	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 37 $	$ - 2^{8} \cdot 3 \cdot 5^{21} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1110$	$16$	$0$	$1$	$1$		$0$	$233280$	$2.355614$	$1736064508952576/3387451171875$	$1.04003$	$5.49194$	$[0, -1, 0, 397467, -148668063]$	$y^2=x^3-x^2+397467x-148668063$	3.4.0.a.1, 15.8.0-3.a.1.1, 222.8.0.?, 1110.16.0.?	$[ ]$	$1$
26640.bg2	26640cd2	26640.bg	26640cd	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 37 $	$ - 2^{8} \cdot 3^{7} \cdot 5^{15} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2220$	$16$	$0$	$0.576005316$	$1$		$4$	$311040$	$2.100201$	$1736064508952576/3387451171875$	$1.04003$	$4.71934$	$[0, 0, 0, 143088, -32083684]$	$y^2=x^3+143088x-32083684$	3.4.0.a.1, 12.8.0-3.a.1.1, 1110.8.0.?, 2220.16.0.?	$[(202, 2250)]$	$1$
33300.i2	33300i2	33300.i	33300i	$2$	$3$	$ 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 37 $	$ - 2^{8} \cdot 3^{7} \cdot 5^{21} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1110$	$16$	$0$	$7.870747831$	$1$		$0$	$1866240$	$2.904919$	$1736064508952576/3387451171875$	$1.04003$	$5.54554$	$[0, 0, 0, 3577200, 4010460500]$	$y^2=x^3+3577200x+4010460500$	3.4.0.a.1, 15.8.0-3.a.1.2, 222.8.0.?, 1110.16.0.?	$[(-1641715/47, 3185546875/47)]$	$1$
35520.bj2	35520n2	35520.bj	35520n	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5 \cdot 37 $	$ - 2^{14} \cdot 3 \cdot 5^{15} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$4440$	$16$	$0$	$1$	$1$		$0$	$311040$	$1.897469$	$1736064508952576/3387451171875$	$1.04003$	$4.35758$	$[0, -1, 0, 63595, -9527475]$	$y^2=x^3-x^2+63595x-9527475$	3.4.0.a.1, 24.8.0-3.a.1.1, 1110.8.0.?, 4440.16.0.?	$[ ]$	$1$
35520.cn2	35520cw2	35520.cn	35520cw	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5 \cdot 37 $	$ - 2^{14} \cdot 3 \cdot 5^{15} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$4440$	$16$	$0$	$1$	$1$		$0$	$311040$	$1.897469$	$1736064508952576/3387451171875$	$1.04003$	$4.35758$	$[0, 1, 0, 63595, 9527475]$	$y^2=x^3+x^2+63595x+9527475$	3.4.0.a.1, 24.8.0-3.a.1.3, 1110.8.0.?, 4440.16.0.?	$[ ]$	$1$
44400.dc2	44400ci2	44400.dc	44400ci	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 37 $	$ - 2^{8} \cdot 3 \cdot 5^{21} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2220$	$16$	$0$	$13.00151382$	$1$		$0$	$933120$	$2.355614$	$1736064508952576/3387451171875$	$1.04003$	$4.78047$	$[0, 1, 0, 397467, 148668063]$	$y^2=x^3+x^2+397467x+148668063$	3.4.0.a.1, 60.8.0-3.a.1.1, 444.8.0.?, 1110.8.0.?, 2220.16.0.?	$[(3292223/49, 6731332350/49)]$	$1$
82140.k2	82140i2	82140.k	82140i	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5 \cdot 37^{2} $	$ - 2^{8} \cdot 3 \cdot 5^{15} \cdot 37^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1110$	$16$	$0$	$1$	$1$		$0$	$13296960$	$3.356354$	$1736064508952576/3387451171875$	$1.04003$	$5.58180$	$[0, 1, 0, 21765275, -60182924377]$	$y^2=x^3+x^2+21765275x-60182924377$	3.4.0.a.1, 30.8.0-3.a.1.1, 111.8.0.?, 1110.16.0.?	$[ ]$	$1$
106560.y2	106560ej2	106560.y	106560ej	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 37 $	$ - 2^{14} \cdot 3^{7} \cdot 5^{15} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$4440$	$16$	$0$	$12.08295758$	$1$		$0$	$2488320$	$2.446774$	$1736064508952576/3387451171875$	$1.04003$	$4.51345$	$[0, 0, 0, 572352, -256669472]$	$y^2=x^3+572352x-256669472$	3.4.0.a.1, 24.8.0-3.a.1.4, 1110.8.0.?, 4440.16.0.?	$[(331121/25, 218337831/25)]$	$1$
106560.cq2	106560bi2	106560.cq	106560bi	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 37 $	$ - 2^{14} \cdot 3^{7} \cdot 5^{15} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$4440$	$16$	$0$	$1$	$1$		$0$	$2488320$	$2.446774$	$1736064508952576/3387451171875$	$1.04003$	$4.51345$	$[0, 0, 0, 572352, 256669472]$	$y^2=x^3+572352x+256669472$	3.4.0.a.1, 24.8.0-3.a.1.2, 1110.8.0.?, 4440.16.0.?	$[ ]$	$1$
108780.t2	108780t2	108780.t	108780t	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 3 \cdot 5^{15} \cdot 7^{6} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$7770$	$16$	$0$	$1.508621266$	$1$		$0$	$3499200$	$2.523849$	$1736064508952576/3387451171875$	$1.04003$	$4.58517$	$[0, -1, 0, 779035, 407321937]$	$y^2=x^3-x^2+779035x+407321937$	3.4.0.a.1, 21.8.0-3.a.1.2, 1110.8.0.?, 7770.16.0.?	$[(7741/2, 765625/2)]$	$1$
133200.fd2	133200dc2	133200.fd	133200dc	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 37 $	$ - 2^{8} \cdot 3^{7} \cdot 5^{21} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2220$	$16$	$0$	$4.094696456$	$1$		$0$	$7464960$	$2.904919$	$1736064508952576/3387451171875$	$1.04003$	$4.89402$	$[0, 0, 0, 3577200, -4010460500]$	$y^2=x^3+3577200x-4010460500$	3.4.0.a.1, 60.8.0-3.a.1.2, 444.8.0.?, 1110.8.0.?, 2220.16.0.?	$[(441365/7, 298828125/7)]$	$1$
177600.dv2	177600ef2	177600.dv	177600ef	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 37 $	$ - 2^{14} \cdot 3 \cdot 5^{21} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$4440$	$16$	$0$	$16.88342758$	$1$		$0$	$7464960$	$2.702187$	$1736064508952576/3387451171875$	$1.04003$	$4.57627$	$[0, -1, 0, 1589867, 1187754637]$	$y^2=x^3-x^2+1589867x+1187754637$	3.4.0.a.1, 120.8.0.?, 888.8.0.?, 1110.8.0.?, 4440.16.0.?	$[(15373344892/4689, 5297915177734375/4689)]$	$1$
177600.fs2	177600fv2	177600.fs	177600fv	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 37 $	$ - 2^{14} \cdot 3 \cdot 5^{21} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$4440$	$16$	$0$	$2.361382214$	$9$	$3$	$0$	$7464960$	$2.702187$	$1736064508952576/3387451171875$	$1.04003$	$4.57627$	$[0, 1, 0, 1589867, -1187754637]$	$y^2=x^3+x^2+1589867x-1187754637$	3.4.0.a.1, 120.8.0.?, 888.8.0.?, 1110.8.0.?, 4440.16.0.?	$[(14182/3, 1953125/3)]$	$1$
246420.k2	246420k2	246420.k	246420k	$2$	$3$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 37^{2} $	$ - 2^{8} \cdot 3^{7} \cdot 5^{15} \cdot 37^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1110$	$16$	$0$	$32.51283982$	$1$		$0$	$106375680$	$3.905659$	$1736064508952576/3387451171875$	$1.04003$	$5.61881$	$[0, 0, 0, 195887472, 1625134845652]$	$y^2=x^3+195887472x+1625134845652$	3.4.0.a.1, 30.8.0-3.a.1.2, 111.8.0.?, 1110.16.0.?	$[(386445892723229/112895, 8565832505267333620317/112895)]$	$1$
268620.y2	268620y2	268620.y	268620y	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 37 $	$ - 2^{8} \cdot 3 \cdot 5^{15} \cdot 11^{6} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$12210$	$16$	$0$	$11.36938498$	$1$		$0$	$13996800$	$2.749844$	$1736064508952576/3387451171875$	$1.04003$	$4.47055$	$[0, 1, 0, 1923739, 1582248039]$	$y^2=x^3+x^2+1923739x+1582248039$	3.4.0.a.1, 33.8.0-3.a.1.1, 1110.8.0.?, 12210.16.0.?	$[(881986/9, 835543115/9)]$	$1$
326340.ba2	326340ba2	326340.ba	326340ba	$2$	$3$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 3^{7} \cdot 5^{15} \cdot 7^{6} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$7770$	$16$	$0$	$12.52334003$	$1$		$0$	$27993600$	$3.073154$	$1736064508952576/3387451171875$	$1.04003$	$4.70761$	$[0, 0, 0, 7011312, -11004703612]$	$y^2=x^3+7011312x-11004703612$	3.4.0.a.1, 21.8.0-3.a.1.1, 1110.8.0.?, 7770.16.0.?	$[(3592057/34, 7937468595/34)]$	$1$
328560.v2	328560v2	328560.v	328560v	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5 \cdot 37^{2} $	$ - 2^{8} \cdot 3 \cdot 5^{15} \cdot 37^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2220$	$16$	$0$	$2.023273502$	$1$		$4$	$53187840$	$3.356354$	$1736064508952576/3387451171875$	$1.04003$	$4.97263$	$[0, -1, 0, 21765275, 60182924377]$	$y^2=x^3-x^2+21765275x+60182924377$	3.4.0.a.1, 60.8.0-3.a.1.4, 444.8.0.?, 1110.8.0.?, 2220.16.0.?	$[(-1491, 156250)]$	$1$
375180.w2	375180w2	375180.w	375180w	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \cdot 37 $	$ - 2^{8} \cdot 3 \cdot 5^{15} \cdot 13^{6} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$14430$	$16$	$0$	$1$	$1$		$0$	$22744800$	$2.833370$	$1736064508952576/3387451171875$	$1.04003$	$4.43227$	$[0, 1, 0, 2686875, -2609765625]$	$y^2=x^3+x^2+2686875x-2609765625$	3.4.0.a.1, 39.8.0-3.a.1.2, 1110.8.0.?, 14430.16.0.?	$[ ]$	$1$
410700.d2	410700d2	410700.d	410700d	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 37^{2} $	$ - 2^{8} \cdot 3 \cdot 5^{21} \cdot 37^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1110$	$16$	$0$	$1$	$9$	$3$	$0$	$319127040$	$4.161072$	$1736064508952576/3387451171875$	$1.04003$	$5.63388$	$[0, -1, 0, 544131867, -7523953810863]$	$y^2=x^3-x^2+544131867x-7523953810863$	3.4.0.a.1, 6.8.0-3.a.1.1, 555.8.0.?, 1110.16.0.?	$[ ]$	$1$
435120.hr2	435120hr2	435120.hr	435120hr	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 3 \cdot 5^{15} \cdot 7^{6} \cdot 37 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$15540$	$16$	$0$	$3.631737017$	$1$		$4$	$13996800$	$2.523849$	$1736064508952576/3387451171875$	$1.04003$	$4.09559$	$[0, 1, 0, 779035, -407321937]$	$y^2=x^3+x^2+779035x-407321937$	3.4.0.a.1, 84.8.0.?, 1110.8.0.?, 15540.16.0.?	$[(1971, 93750), (34651/9, 1531250/9)]$	$1$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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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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