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

Intrinsic torsion order

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Results (24 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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
4640.c1	4640b1	4640.c	4640b	$2$	$2$	$ 2^{5} \cdot 5 \cdot 29 $	$ 2^{6} \cdot 5 \cdot 29 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.22	2B	$1160$	$48$	$0$	$5.130390670$	$1$		$1$	$384$	$-0.087988$	$12422690496/145$	$0.99973$	$3.24569$	$2$	$[0, 0, 0, -193, -1032]$	$y^2=x^3-193x-1032$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 290.6.0.?, 580.12.0.?, $\ldots$	$[(137/2, 1443/2)]$	$1$
4640.d1	4640a1	4640.d	4640a	$2$	$2$	$ 2^{5} \cdot 5 \cdot 29 $	$ 2^{6} \cdot 5 \cdot 29 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.22	2B	$1160$	$48$	$0$	$1.912891315$	$1$		$3$	$384$	$-0.087988$	$12422690496/145$	$0.99973$	$3.24569$	$2$	$[0, 0, 0, -193, 1032]$	$y^2=x^3-193x+1032$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 290.6.0.?, 580.12.0.?, $\ldots$	$[(4, 18)]$	$1$
9280.j1	9280s2	9280.j	9280s	$2$	$2$	$ 2^{6} \cdot 5 \cdot 29 $	$ 2^{12} \cdot 5 \cdot 29 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.21	2B	$1160$	$48$	$0$	$1$	$1$		$1$	$1536$	$0.258585$	$12422690496/145$	$0.99973$	$3.45467$	$2$	$[0, 0, 0, -772, -8256]$	$y^2=x^3-772x-8256$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.3, 290.6.0.?, 580.12.0.?, $\ldots$	$[ ]$	$1$
9280.p1	9280p2	9280.p	9280p	$2$	$2$	$ 2^{6} \cdot 5 \cdot 29 $	$ 2^{12} \cdot 5 \cdot 29 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.21	2B	$1160$	$48$	$0$	$1$	$1$		$1$	$1536$	$0.258585$	$12422690496/145$	$0.99973$	$3.45467$	$2$	$[0, 0, 0, -772, 8256]$	$y^2=x^3-772x+8256$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.3, 290.6.0.?, 580.12.0.?, $\ldots$	$[ ]$	$1$
23200.f1	23200f1	23200.f	23200f	$2$	$2$	$ 2^{5} \cdot 5^{2} \cdot 29 $	$ 2^{6} \cdot 5^{7} \cdot 29 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$1160$	$48$	$0$	$4.275275756$	$1$		$9$	$9216$	$0.716730$	$12422690496/145$	$0.99973$	$3.68669$	$2$	$[0, 0, 0, -4825, 129000]$	$y^2=x^3-4825x+129000$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.2, 232.12.0.?, 290.6.0.?, $\ldots$	$[(39, 12), (31, 96)]$	$1$
23200.g1	23200e1	23200.g	23200e	$2$	$2$	$ 2^{5} \cdot 5^{2} \cdot 29 $	$ 2^{6} \cdot 5^{7} \cdot 29 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$1160$	$48$	$0$	$1$	$4$	$2$	$1$	$9216$	$0.716730$	$12422690496/145$	$0.99973$	$3.68669$	$2$	$[0, 0, 0, -4825, -129000]$	$y^2=x^3-4825x-129000$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.2, 232.12.0.?, 290.6.0.?, $\ldots$	$[ ]$	$1$
41760.v1	41760bn1	41760.v	41760bn	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 29 $	$ 2^{6} \cdot 3^{6} \cdot 5 \cdot 29 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3480$	$48$	$0$	$1.390123021$	$1$		$5$	$12288$	$0.461318$	$12422690496/145$	$0.99973$	$3.19496$	$2$	$[0, 0, 0, -1737, 27864]$	$y^2=x^3-1737x+27864$	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.4, 290.6.0.?, 580.12.0.?, $\ldots$	$[(25, 8)]$	$1$
41760.bk1	41760bm1	41760.bk	41760bm	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 29 $	$ 2^{6} \cdot 3^{6} \cdot 5 \cdot 29 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3480$	$48$	$0$	$4.783694125$	$1$		$3$	$12288$	$0.461318$	$12422690496/145$	$0.99973$	$3.19496$	$2$	$[0, 0, 0, -1737, -27864]$	$y^2=x^3-1737x-27864$	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.4, 290.6.0.?, 580.12.0.?, $\ldots$	$[(145, 1664)]$	$1$
46400.be1	46400bq2	46400.be	46400bq	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 29 $	$ 2^{12} \cdot 5^{7} \cdot 29 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$1160$	$48$	$0$	$1.100027832$	$1$		$7$	$36864$	$1.063305$	$12422690496/145$	$0.99973$	$3.83592$	$2$	$[0, 0, 0, -19300, 1032000]$	$y^2=x^3-19300x+1032000$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.3, 232.12.0.?, 290.6.0.?, $\ldots$	$[(85, 75)]$	$1$
46400.bo1	46400bp2	46400.bo	46400bp	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 29 $	$ 2^{12} \cdot 5^{7} \cdot 29 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$1160$	$48$	$0$	$3.490308965$	$1$		$3$	$36864$	$1.063305$	$12422690496/145$	$0.99973$	$3.83592$	$2$	$[0, 0, 0, -19300, -1032000]$	$y^2=x^3-19300x-1032000$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.3, 232.12.0.?, 290.6.0.?, $\ldots$	$[(165, 525)]$	$1$
83520.v1	83520em2	83520.v	83520em	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 29 $	$ 2^{12} \cdot 3^{6} \cdot 5 \cdot 29 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3480$	$48$	$0$	$0.794824653$	$1$		$7$	$49152$	$0.807891$	$12422690496/145$	$0.99973$	$3.36652$	$2$	$[0, 0, 0, -6948, 222912]$	$y^2=x^3-6948x+222912$	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.1, 290.6.0.?, 580.12.0.?, $\ldots$	$[(54, 72)]$	$1$
83520.cj1	83520eh2	83520.cj	83520eh	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 29 $	$ 2^{12} \cdot 3^{6} \cdot 5 \cdot 29 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3480$	$48$	$0$	$2.873133428$	$1$		$3$	$49152$	$0.807891$	$12422690496/145$	$0.99973$	$3.36652$	$2$	$[0, 0, 0, -6948, -222912]$	$y^2=x^3-6948x-222912$	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.1, 290.6.0.?, 580.12.0.?, $\ldots$	$[(102, 360)]$	$1$
134560.h1	134560c1	134560.h	134560c	$2$	$2$	$ 2^{5} \cdot 5 \cdot 29^{2} $	$ 2^{6} \cdot 5 \cdot 29^{7} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$1160$	$48$	$0$	$41.67061964$	$1$		$5$	$322560$	$1.595659$	$12422690496/145$	$0.99973$	$4.03102$	$2$	$[0, 0, 0, -162313, -25169448]$	$y^2=x^3-162313x-25169448$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.4, 232.12.0.?, 290.6.0.?, $\ldots$	$[(-233, 12), (-17875657/277, 268262904/277)]$	$1$
134560.i1	134560d1	134560.i	134560d	$2$	$2$	$ 2^{5} \cdot 5 \cdot 29^{2} $	$ 2^{6} \cdot 5 \cdot 29^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$1160$	$48$	$0$	$1$	$4$	$2$	$1$	$322560$	$1.595659$	$12422690496/145$	$0.99973$	$4.03102$	$2$	$[0, 0, 0, -162313, 25169448]$	$y^2=x^3-162313x+25169448$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.4, 232.12.0.?, 290.6.0.?, $\ldots$	$[ ]$	$1$
208800.s1	208800cc1	208800.s	208800cc	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 29 $	$ 2^{6} \cdot 3^{6} \cdot 5^{7} \cdot 29 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3480$	$48$	$0$	$2.547673456$	$1$		$3$	$294912$	$1.266037$	$12422690496/145$	$0.99973$	$3.56352$	$2$	$[0, 0, 0, -43425, -3483000]$	$y^2=x^3-43425x-3483000$	2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 290.6.0.?, 580.12.0.?, $\ldots$	$[(285, 2700)]$	$1$
208800.cm1	208800cr1	208800.cm	208800cr	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 29 $	$ 2^{6} \cdot 3^{6} \cdot 5^{7} \cdot 29 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3480$	$48$	$0$	$1.026646864$	$1$		$7$	$294912$	$1.266037$	$12422690496/145$	$0.99973$	$3.56352$	$2$	$[0, 0, 0, -43425, 3483000]$	$y^2=x^3-43425x+3483000$	2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 290.6.0.?, 580.12.0.?, $\ldots$	$[(115, 100)]$	$1$
227360.r1	227360w1	227360.r	227360w	$2$	$2$	$ 2^{5} \cdot 5 \cdot 7^{2} \cdot 29 $	$ 2^{6} \cdot 5 \cdot 7^{6} \cdot 29 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$8120$	$48$	$0$	$14.53590794$	$1$		$1$	$138240$	$0.884967$	$12422690496/145$	$0.99973$	$3.16817$	$2$	$[0, 0, 0, -9457, -353976]$	$y^2=x^3-9457x-353976$	2.3.0.a.1, 4.6.0.b.1, 56.12.0-4.b.1.2, 290.6.0.?, 580.12.0.?, $\ldots$	$[(1375889/110, 269276463/110)]$	$1$
227360.x1	227360y1	227360.x	227360y	$2$	$2$	$ 2^{5} \cdot 5 \cdot 7^{2} \cdot 29 $	$ 2^{6} \cdot 5 \cdot 7^{6} \cdot 29 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$8120$	$48$	$0$	$4.415792370$	$1$		$1$	$138240$	$0.884967$	$12422690496/145$	$0.99973$	$3.16817$	$2$	$[0, 0, 0, -9457, 353976]$	$y^2=x^3-9457x+353976$	2.3.0.a.1, 4.6.0.b.1, 56.12.0-4.b.1.2, 290.6.0.?, 580.12.0.?, $\ldots$	$[(249/2, 645/2)]$	$1$
269120.bm1	269120bm2	269120.bm	269120bm	$2$	$2$	$ 2^{6} \cdot 5 \cdot 29^{2} $	$ 2^{12} \cdot 5 \cdot 29^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$1160$	$48$	$0$	$9.370874536$	$1$		$1$	$1290240$	$1.942232$	$12422690496/145$	$0.99973$	$4.14018$	$2$	$[0, 0, 0, -649252, -201355584]$	$y^2=x^3-649252x-201355584$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.1, 232.12.0.?, 290.6.0.?, $\ldots$	$[(544069/23, 179978205/23)]$	$1$
269120.bq1	269120bq2	269120.bq	269120bq	$2$	$2$	$ 2^{6} \cdot 5 \cdot 29^{2} $	$ 2^{12} \cdot 5 \cdot 29^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$1160$	$48$	$0$	$3.479246089$	$1$		$1$	$1290240$	$1.942232$	$12422690496/145$	$0.99973$	$4.14018$	$2$	$[0, 0, 0, -649252, 201355584]$	$y^2=x^3-649252x+201355584$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.1, 232.12.0.?, 290.6.0.?, $\ldots$	$[(1276/3, 285940/3)]$	$1$
417600.dt1	417600dt2	417600.dt	417600dt	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 $	$ 2^{12} \cdot 3^{6} \cdot 5^{7} \cdot 29 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3480$	$48$	$0$	$4.450075608$	$1$		$3$	$1179648$	$1.612610$	$12422690496/145$	$0.99973$	$3.69401$	$2$	$[0, 0, 0, -173700, -27864000]$	$y^2=x^3-173700x-27864000$	2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 290.6.0.?, 580.12.0.?, $\ldots$	$[(486, 1584)]$	$1$
417600.mf1	417600mf2	417600.mf	417600mf	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 $	$ 2^{12} \cdot 3^{6} \cdot 5^{7} \cdot 29 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3480$	$48$	$0$	$1.708500720$	$1$		$5$	$1179648$	$1.612610$	$12422690496/145$	$0.99973$	$3.69401$	$2$	$[0, 0, 0, -173700, 27864000]$	$y^2=x^3-173700x+27864000$	2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 290.6.0.?, 580.12.0.?, $\ldots$	$[(90, 3600)]$	$1$
454720.bw1	454720bw2	454720.bw	454720bw	$2$	$2$	$ 2^{6} \cdot 5 \cdot 7^{2} \cdot 29 $	$ 2^{12} \cdot 5 \cdot 7^{6} \cdot 29 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$8120$	$48$	$0$	$1$	$1$		$1$	$552960$	$1.231541$	$12422690496/145$	$0.99973$	$3.31884$	$2$	$[0, 0, 0, -37828, 2831808]$	$y^2=x^3-37828x+2831808$	2.3.0.a.1, 4.6.0.b.1, 56.12.0-4.b.1.3, 290.6.0.?, 580.12.0.?, $\ldots$	$[ ]$	$1$
454720.cn1	454720cn2	454720.cn	454720cn	$2$	$2$	$ 2^{6} \cdot 5 \cdot 7^{2} \cdot 29 $	$ 2^{12} \cdot 5 \cdot 7^{6} \cdot 29 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$8120$	$48$	$0$	$1$	$1$		$1$	$552960$	$1.231541$	$12422690496/145$	$0.99973$	$3.31884$	$2$	$[0, 0, 0, -37828, -2831808]$	$y^2=x^3-37828x-2831808$	2.3.0.a.1, 4.6.0.b.1, 56.12.0-4.b.1.3, 290.6.0.?, 580.12.0.?, $\ldots$	$[ ]$	$1$

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

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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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