LMFDB - Elliptic curve search results

Refine search

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

		Sort order	Select

Results (22 matches)

Download displayed columns for results to

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	Semistable	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
2415.b2	2415f2	2415.b	2415f	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.6.0.1	2Cs	$9660$	$48$	$0$	$1$	$1$	$2$	$2112$	$0.738904$	$2630872462131649/3645140625$	$1.01084$	$4.55823$	$[1, 0, 0, -2876, 59055]$	$y^2+xy=x^3-2876x+59055$	2.6.0.a.1, 28.12.0-2.a.1.1, 60.12.0-2.a.1.1, 92.12.0.?, 420.24.0.?, $\ldots$	$[]$
7245.s2	7245s2	7245.s	7245s	$4$	$4$	$ 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ 3^{8} \cdot 5^{6} \cdot 7^{2} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$9660$	$48$	$0$	$1$	$1$	$2$	$16896$	$1.288210$	$2630872462131649/3645140625$	$1.01084$	$4.73644$	$[1, -1, 0, -25884, -1594485]$	$y^2+xy=x^3-x^2-25884x-1594485$	2.6.0.a.1, 20.12.0-2.a.1.1, 84.12.0.?, 276.12.0.?, 420.24.0.?, $\ldots$	$[]$
12075.r2	12075c2	12075.r	12075c	$4$	$4$	$ 3 \cdot 5^{2} \cdot 7 \cdot 23 $	$ 3^{2} \cdot 5^{12} \cdot 7^{2} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$9660$	$48$	$0$	$3.547983861$	$1$	$4$	$50688$	$1.543623$	$2630872462131649/3645140625$	$1.01084$	$4.80511$	$[1, 1, 0, -71900, 7381875]$	$y^2+xy=x^3+x^2-71900x+7381875$	2.6.0.a.1, 12.12.0-2.a.1.1, 140.12.0.?, 420.24.0.?, 460.12.0.?, $\ldots$	$[(794, 20855)]$
16905.g2	16905q2	16905.g	16905q	$4$	$4$	$ 3 \cdot 5 \cdot 7^{2} \cdot 23 $	$ 3^{2} \cdot 5^{6} \cdot 7^{8} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.12.0.1	2Cs	$9660$	$48$	$0$	$1$	$1$	$2$	$101376$	$1.711859$	$2630872462131649/3645140625$	$1.01084$	$4.84641$	$[1, 1, 1, -140925, -20396790]$	$y^2+xy+y=x^3+x^2-140925x-20396790$	2.6.0.a.1, 4.12.0-2.a.1.1, 420.24.0.?, 644.24.0.?, 1380.24.0.?, $\ldots$	$[]$
36225.l2	36225bk2	36225.l	36225bk	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 $	$ 3^{8} \cdot 5^{12} \cdot 7^{2} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.12.0.1	2Cs	$9660$	$48$	$0$	$3.425587478$	$1$	$4$	$405504$	$2.092930$	$2630872462131649/3645140625$	$1.01084$	$4.93016$	$[1, -1, 1, -647105, -199957728]$	$y^2+xy+y=x^3-x^2-647105x-199957728$	2.6.0.a.1, 4.12.0-2.a.1.1, 420.24.0.?, 644.24.0.?, 1380.24.0.?, $\ldots$	$[(1649, 55875)]$
38640.d2	38640bg2	38640.d	38640bg	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 23 $	$ 2^{12} \cdot 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$9660$	$48$	$0$	$1$	$1$	$3$	$135168$	$1.432051$	$2630872462131649/3645140625$	$1.01084$	$4.14918$	$[0, -1, 0, -46016, -3779520]$	$y^2=x^3-x^2-46016x-3779520$	2.6.0.a.1, 28.12.0-2.a.1.1, 60.12.0-2.a.1.1, 92.12.0.?, 420.24.0.?, $\ldots$	$[]$
50715.bi2	50715q2	50715.bi	50715q	$4$	$4$	$ 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 $	$ 3^{8} \cdot 5^{6} \cdot 7^{8} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$9660$	$48$	$0$	$3.986951791$	$1$	$4$	$811008$	$2.261166$	$2630872462131649/3645140625$	$1.01084$	$4.96339$	$[1, -1, 0, -1268325, 549445000]$	$y^2+xy=x^3-x^2-1268325x+549445000$	2.6.0.a.1, 12.12.0-2.a.1.1, 140.12.0.?, 420.24.0.?, 460.12.0.?, $\ldots$	$[(-472, 32528)]$
55545.g2	55545u2	55545.g	55545u	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23^{2} $	$ 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 23^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.12.0.1	2Cs	$9660$	$48$	$0$	$1$	$1$	$2$	$1115136$	$2.306652$	$2630872462131649/3645140625$	$1.01084$	$4.97202$	$[1, 0, 0, -1521415, -721565008]$	$y^2+xy=x^3-1521415x-721565008$	2.6.0.a.1, 4.12.0-2.a.1.1, 420.24.0.?, 644.24.0.?, 1380.24.0.?, $\ldots$	$[]$
84525.da2	84525by2	84525.da	84525by	$4$	$4$	$ 3 \cdot 5^{2} \cdot 7^{2} \cdot 23 $	$ 3^{2} \cdot 5^{12} \cdot 7^{8} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$9660$	$48$	$0$	$23.89134276$	$1$	$2$	$2433024$	$2.516579$	$2630872462131649/3645140625$	$1.01084$	$5.01006$	$[1, 0, 1, -3523126, -2542552477]$	$y^2+xy+y=x^3-3523126x-2542552477$	2.6.0.a.1, 20.12.0-2.a.1.1, 84.12.0.?, 276.12.0.?, 420.24.0.?, $\ldots$	$[(3313825262497/21424, 5768496027926174999/21424)]$
115920.dr2	115920en2	115920.dr	115920en	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{12} \cdot 3^{8} \cdot 5^{6} \cdot 7^{2} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$9660$	$48$	$0$	$0.899528152$	$1$	$13$	$1081344$	$1.981358$	$2630872462131649/3645140625$	$1.01084$	$4.32356$	$[0, 0, 0, -414147, 102461186]$	$y^2=x^3-414147x+102461186$	2.6.0.a.1, 20.12.0-2.a.1.1, 84.12.0.?, 276.12.0.?, 420.24.0.?, $\ldots$	$[(407, 1150)]$
154560.dd2	154560ga2	154560.dd	154560ga	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 $	$ 2^{18} \cdot 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 23^{2} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$19320$	$48$	$0$	$1.950004065$	$1$	$29$	$1081344$	$1.778625$	$2630872462131649/3645140625$	$1.01084$	$4.01585$	$[0, -1, 0, -184065, 30420225]$	$y^2=x^3-x^2-184065x+30420225$	2.6.0.a.1, 56.12.0-2.a.1.1, 120.12.0.?, 184.12.0.?, 420.12.0.?, $\ldots$	$[(80, 4025), (-15, 5760)]$
154560.hd2	154560ba2	154560.hd	154560ba	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 $	$ 2^{18} \cdot 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$19320$	$48$	$0$	$1$	$1$	$3$	$1081344$	$1.778625$	$2630872462131649/3645140625$	$1.01084$	$4.01585$	$[0, 1, 0, -184065, -30420225]$	$y^2=x^3+x^2-184065x-30420225$	2.6.0.a.1, 56.12.0-2.a.1.1, 120.12.0.?, 184.12.0.?, 420.12.0.?, $\ldots$	$[]$
166635.bi2	166635bw2	166635.bi	166635bw	$4$	$4$	$ 3^{2} \cdot 5 \cdot 7 \cdot 23^{2} $	$ 3^{8} \cdot 5^{6} \cdot 7^{2} \cdot 23^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$9660$	$48$	$0$	$10.36512053$	$1$	$2$	$8921088$	$2.855957$	$2630872462131649/3645140625$	$1.01084$	$5.06595$	$[1, -1, 0, -13692735, 19482255216]$	$y^2+xy=x^3-x^2-13692735x+19482255216$	2.6.0.a.1, 12.12.0-2.a.1.1, 140.12.0.?, 420.24.0.?, 460.12.0.?, $\ldots$	$[(998715/22, 23663127/22)]$
193200.fx2	193200y2	193200.fx	193200y	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 $	$ 2^{12} \cdot 3^{2} \cdot 5^{12} \cdot 7^{2} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$9660$	$48$	$0$	$7.845161622$	$1$	$3$	$3244032$	$2.236771$	$2630872462131649/3645140625$	$1.01084$	$4.39392$	$[0, 1, 0, -1150408, -474740812]$	$y^2=x^3+x^2-1150408x-474740812$	2.6.0.a.1, 12.12.0-2.a.1.1, 140.12.0.?, 420.24.0.?, 460.12.0.?, $\ldots$	$[(18916/3, 2159378/3)]$
253575.ba2	253575ba2	253575.ba	253575ba	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 23 $	$ 3^{8} \cdot 5^{12} \cdot 7^{8} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$9660$	$48$	$0$	$1$	$1$	$2$	$19464192$	$3.065884$	$2630872462131649/3645140625$	$1.01084$	$5.09746$	$[1, -1, 1, -31708130, 68648916872]$	$y^2+xy+y=x^3-x^2-31708130x+68648916872$	2.6.0.a.1, 28.12.0-2.a.1.1, 60.12.0-2.a.1.1, 92.12.0.?, 420.24.0.?, $\ldots$	$[]$
270480.hj2	270480hj2	270480.hj	270480hj	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 $	$ 2^{12} \cdot 3^{2} \cdot 5^{6} \cdot 7^{8} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.12.0.1	2Cs	$9660$	$48$	$0$	$1.537973510$	$1$	$9$	$6488064$	$2.405006$	$2630872462131649/3645140625$	$1.01084$	$4.43712$	$[0, 1, 0, -2254800, 1300884948]$	$y^2=x^3+x^2-2254800x+1300884948$	2.6.0.a.1, 4.12.0-2.a.1.1, 420.24.0.?, 644.24.0.?, 1380.24.0.?, $\ldots$	$[(716, 7350)]$
277725.cg2	277725cg2	277725.cg	277725cg	$4$	$4$	$ 3 \cdot 5^{2} \cdot 7 \cdot 23^{2} $	$ 3^{2} \cdot 5^{12} \cdot 7^{2} \cdot 23^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$9660$	$48$	$0$	$22.81497795$	$1$	$2$	$26763264$	$3.111370$	$2630872462131649/3645140625$	$1.01084$	$5.10401$	$[1, 1, 0, -38035375, -90195626000]$	$y^2+xy=x^3+x^2-38035375x-90195626000$	2.6.0.a.1, 20.12.0-2.a.1.1, 84.12.0.?, 276.12.0.?, 420.24.0.?, $\ldots$	$[(-1098755289005/17574, 66065459402549435/17574)]$
292215.bd2	292215bd2	292215.bd	292215bd	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 23 $	$ 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 11^{6} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$106260$	$48$	$0$	$1$	$1$	$2$	$2703360$	$1.937851$	$2630872462131649/3645140625$	$1.01084$	$3.96444$	$[1, 0, 1, -347999, -78950203]$	$y^2+xy+y=x^3-347999x-78950203$	2.6.0.a.1, 308.12.0.?, 420.12.0.?, 644.12.0.?, 660.12.0.?, $\ldots$	$[]$
388815.o2	388815o2	388815.o	388815o	$4$	$4$	$ 3 \cdot 5 \cdot 7^{2} \cdot 23^{2} $	$ 3^{2} \cdot 5^{6} \cdot 7^{8} \cdot 23^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$9660$	$48$	$0$	$5.904140198$	$1$	$4$	$53526528$	$3.279606$	$2630872462131649/3645140625$	$1.01084$	$5.12744$	$[1, 1, 1, -74549336, 247422248408]$	$y^2+xy+y=x^3+x^2-74549336x+247422248408$	2.6.0.a.1, 28.12.0-2.a.1.1, 60.12.0-2.a.1.2, 92.12.0.?, 420.24.0.?, $\ldots$	$[(783531, 693127234)]$
408135.bs2	408135bs2	408135.bs	408135bs	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 13^{2} \cdot 23 $	$ 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 13^{6} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$125580$	$48$	$0$	$1$	$1$	$2$	$4866048$	$2.021378$	$2630872462131649/3645140625$	$1.01084$	$3.93950$	$[1, 0, 1, -486048, 130229881]$	$y^2+xy+y=x^3-486048x+130229881$	2.6.0.a.1, 364.12.0.?, 420.12.0.?, 644.12.0.?, 780.12.0.?, $\ldots$	$[]$
463680.k2	463680k2	463680.k	463680k	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{18} \cdot 3^{8} \cdot 5^{6} \cdot 7^{2} \cdot 23^{2} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$19320$	$48$	$0$	$6.360810674$	$1$	$21$	$8650752$	$2.327930$	$2630872462131649/3645140625$	$1.01084$	$4.18293$	$[0, 0, 0, -1656588, 819689488]$	$y^2=x^3-1656588x+819689488$	2.6.0.a.1, 40.12.0-2.a.1.1, 168.12.0.?, 420.12.0.?, 552.12.0.?, $\ldots$	$[(818, 3456), (701, 1701)]$
463680.gt2	463680gt2	463680.gt	463680gt	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{18} \cdot 3^{8} \cdot 5^{6} \cdot 7^{2} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.6.0.1	2Cs	$19320$	$48$	$0$	$8.182836214$	$1$	$5$	$8650752$	$2.327930$	$2630872462131649/3645140625$	$1.01084$	$4.18293$	$[0, 0, 0, -1656588, -819689488]$	$y^2=x^3-1656588x-819689488$	2.6.0.a.1, 40.12.0-2.a.1.1, 168.12.0.?, 420.12.0.?, 552.12.0.?, $\ldots$	$[(316861, 178360875)]$

Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (22 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Learn more

Refine search Advanced search options

Results (22 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Refine search