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	Manin constant

		Sort order	Select

Results (20 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
4290.bc4	4290bc2	4290.bc	4290bc	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13 $	$ 2^{12} \cdot 3^{4} \cdot 5^{2} \cdot 11^{4} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.48.0.26	2Cs	$17160$	$192$	$1$	$1$	$1$	$6$	$15360$	$1.357813$	$1402524686897642881/20523074457600$	$0.96787$	$4.99577$	$[1, 0, 0, -23320, -1355200]$	$y^2+xy=x^3-23320x-1355200$	2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.d.2.1, 260.48.0.?, 264.96.0.?, $\ldots$	$[ ]$
12870.f4	12870k2	12870.f	12870k	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{12} \cdot 3^{10} \cdot 5^{2} \cdot 11^{4} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.13	2Cs	$17160$	$192$	$1$	$2.003926709$	$1$	$8$	$122880$	$1.907120$	$1402524686897642881/20523074457600$	$0.96787$	$5.11236$	$[1, -1, 0, -209880, 36590400]$	$y^2+xy=x^3-x^2-209880x+36590400$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.2, 12.24.0-4.b.1.3, 24.48.0-8.d.2.2, $\ldots$	$[(201, 1479)]$
21450.k4	21450f2	21450.k	21450f	$6$	$8$	$ 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 $	$ 2^{12} \cdot 3^{4} \cdot 5^{8} \cdot 11^{4} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.13	2Cs	$17160$	$192$	$1$	$1$	$1$	$2$	$368640$	$2.162533$	$1402524686897642881/20523074457600$	$0.96787$	$5.15782$	$[1, 1, 0, -583000, -169400000]$	$y^2+xy=x^3+x^2-583000x-169400000$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.2, 20.24.0-4.b.1.3, 40.48.0-8.d.2.1, $\ldots$	$[ ]$
34320.u4	34320bh2	34320.u	34320bh	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 13 $	$ 2^{24} \cdot 3^{4} \cdot 5^{2} \cdot 11^{4} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.48.0.33	2Cs	$17160$	$192$	$1$	$1$	$1$	$3$	$368640$	$2.050961$	$1402524686897642881/20523074457600$	$0.96787$	$4.79750$	$[0, -1, 0, -373120, 86732800]$	$y^2=x^3-x^2-373120x+86732800$	2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.d.2.2, 260.48.0.?, 264.96.0.?, $\ldots$	$[ ]$
47190.bi4	47190bg2	47190.bi	47190bg	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 11^{2} \cdot 13 $	$ 2^{12} \cdot 3^{4} \cdot 5^{2} \cdot 11^{10} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.13	2Cs	$17160$	$192$	$1$	$1$	$1$	$2$	$1843200$	$2.556763$	$1402524686897642881/20523074457600$	$0.96787$	$5.21952$	$[1, 0, 1, -2821723, 1800949478]$	$y^2+xy+y=x^3-2821723x+1800949478$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.2, 24.48.0-8.d.2.8, 44.24.0-4.b.1.3, $\ldots$	$[ ]$
55770.y4	55770u2	55770.y	55770u	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13^{2} $	$ 2^{12} \cdot 3^{4} \cdot 5^{2} \cdot 11^{4} \cdot 13^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.13	2Cs	$17160$	$192$	$1$	$1$	$1$	$2$	$2580480$	$2.640289$	$1402524686897642881/20523074457600$	$0.96787$	$5.23145$	$[1, 0, 1, -3941084, -2973433318]$	$y^2+xy+y=x^3-3941084x-2973433318$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.2, 20.24.0-4.b.1.2, 40.48.0-8.d.2.16, $\ldots$	$[ ]$
64350.dr4	64350dj2	64350.dr	64350dj	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13 $	$ 2^{12} \cdot 3^{10} \cdot 5^{8} \cdot 11^{4} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.13	2Cs	$17160$	$192$	$1$	$1.211188044$	$1$	$12$	$2949120$	$2.711838$	$1402524686897642881/20523074457600$	$0.96787$	$5.24139$	$[1, -1, 1, -5247005, 4568552997]$	$y^2+xy+y=x^3-x^2-5247005x+4568552997$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.2, 60.24.0-4.b.1.3, 120.48.0.?, $\ldots$	$[(599, 40200)]$
102960.bl4	102960dt2	102960.bl	102960dt	$6$	$8$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{24} \cdot 3^{10} \cdot 5^{2} \cdot 11^{4} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.13	2Cs	$17160$	$192$	$1$	$3.087023768$	$1$	$7$	$2949120$	$2.600266$	$1402524686897642881/20523074457600$	$0.96787$	$4.91195$	$[0, 0, 0, -3358083, -2338427518]$	$y^2=x^3-3358083x-2338427518$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.2, 12.24.0-4.b.1.1, 24.48.0-8.d.2.1, $\ldots$	$[(-1121, 4158)]$
137280.n4	137280ha2	137280.n	137280ha	$6$	$8$	$ 2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 13 $	$ 2^{30} \cdot 3^{4} \cdot 5^{2} \cdot 11^{4} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.48.0.118	2Cs	$17160$	$192$	$1$	$9.514632856$	$1$	$5$	$2949120$	$2.397533$	$1402524686897642881/20523074457600$	$0.96787$	$4.58685$	$[0, -1, 0, -1492481, -692369919]$	$y^2=x^3-x^2-1492481x-692369919$	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.d.2.6, 260.24.0.?, 264.96.0.?, $\ldots$	$[(217891, 101707060)]$
137280.ez4	137280bg2	137280.ez	137280bg	$6$	$8$	$ 2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 13 $	$ 2^{30} \cdot 3^{4} \cdot 5^{2} \cdot 11^{4} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.48.0.72	2Cs	$17160$	$192$	$1$	$1$	$1$	$3$	$2949120$	$2.397533$	$1402524686897642881/20523074457600$	$0.96787$	$4.58685$	$[0, 1, 0, -1492481, 692369919]$	$y^2=x^3+x^2-1492481x+692369919$	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.d.2.5, 260.24.0.?, 264.96.0.?, $\ldots$	$[ ]$
141570.dg4	141570bs2	141570.dg	141570bs	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13 $	$ 2^{12} \cdot 3^{10} \cdot 5^{2} \cdot 11^{10} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.48.0.73	2Cs	$17160$	$192$	$1$	$1$	$1$	$2$	$14745600$	$3.106068$	$1402524686897642881/20523074457600$	$0.96787$	$5.29182$	$[1, -1, 1, -25395503, -48625635913]$	$y^2+xy+y=x^3-x^2-25395503x-48625635913$	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.d.2.7, 132.24.0.?, 260.24.0.?, $\ldots$	$[ ]$
167310.fe4	167310k2	167310.fe	167310k	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13^{2} $	$ 2^{12} \cdot 3^{10} \cdot 5^{2} \cdot 11^{4} \cdot 13^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.13	2Cs	$17160$	$192$	$1$	$1.216878904$	$1$	$12$	$20643840$	$3.189594$	$1402524686897642881/20523074457600$	$0.96787$	$5.30165$	$[1, -1, 1, -35469752, 80282699579]$	$y^2+xy+y=x^3-x^2-35469752x+80282699579$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.2, 60.24.0-4.b.1.2, 120.48.0.?, $\ldots$	$[(4287, 81511)]$
171600.fr4	171600bv2	171600.fr	171600bv	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 $	$ 2^{24} \cdot 3^{4} \cdot 5^{8} \cdot 11^{4} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.13	2Cs	$17160$	$192$	$1$	$3.280777751$	$1$	$9$	$8847360$	$2.855679$	$1402524686897642881/20523074457600$	$0.96787$	$4.95807$	$[0, 1, 0, -9328008, 10822943988]$	$y^2=x^3+x^2-9328008x+10822943988$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.2, 20.24.0-4.b.1.1, 40.48.0-8.d.2.2, $\ldots$	$[(1548, 9750)]$
210210.cx4	210210cr2	210210.cx	210210cr	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \cdot 13 $	$ 2^{12} \cdot 3^{4} \cdot 5^{2} \cdot 7^{6} \cdot 11^{4} \cdot 13^{2} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.13	2Cs	$120120$	$192$	$1$	$0.678453157$	$1$	$50$	$5898240$	$2.330769$	$1402524686897642881/20523074457600$	$0.96787$	$4.36202$	$[1, 1, 1, -1142681, 463690919]$	$y^2+xy+y=x^3+x^2-1142681x+463690919$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.2, 28.24.0-4.b.1.3, 56.48.0-8.d.2.2, $\ldots$	$[(-1, 21560), (461, 5698)]$
235950.fs4	235950fs2	235950.fs	235950fs	$6$	$8$	$ 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 13 $	$ 2^{12} \cdot 3^{4} \cdot 5^{8} \cdot 11^{10} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.13	2Cs	$17160$	$192$	$1$	$1$	$1$	$2$	$44236800$	$3.361481$	$1402524686897642881/20523074457600$	$0.96787$	$5.32106$	$[1, 1, 1, -70543063, 225118684781]$	$y^2+xy+y=x^3+x^2-70543063x+225118684781$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.2, 120.48.0.?, 220.24.0.?, $\ldots$	$[ ]$
278850.fs4	278850fs2	278850.fs	278850fs	$6$	$8$	$ 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13^{2} $	$ 2^{12} \cdot 3^{4} \cdot 5^{8} \cdot 11^{4} \cdot 13^{8} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.48.0.12	2Cs	$17160$	$192$	$1$	$8.207501642$	$1$	$18$	$61931520$	$3.445007$	$1402524686897642881/20523074457600$	$0.96787$	$5.33010$	$[1, 1, 1, -98527088, -371679164719]$	$y^2+xy+y=x^3+x^2-98527088x-371679164719$	2.6.0.a.1, 4.24.0-4.b.1.2, 8.48.0-8.d.2.16, 260.48.0.?, 264.96.0.?, $\ldots$	$[(-5979, 63973), (-6195, 34597)]$
377520.cn4	377520cn2	377520.cn	377520cn	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 13 $	$ 2^{24} \cdot 3^{4} \cdot 5^{2} \cdot 11^{10} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.13	2Cs	$17160$	$192$	$1$	$1$	$1$	$3$	$44236800$	$3.249908$	$1402524686897642881/20523074457600$	$0.96787$	$5.02204$	$[0, -1, 0, -45147560, -115260766608]$	$y^2=x^3-x^2-45147560x-115260766608$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.2, 24.48.0-8.d.2.7, 44.24.0-4.b.1.1, $\ldots$	$[ ]$
411840.jr4	411840jr2	411840.jr	411840jr	$6$	$8$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{30} \cdot 3^{10} \cdot 5^{2} \cdot 11^{4} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.13	2Cs	$17160$	$192$	$1$	$1$	$1$	$3$	$23592960$	$2.946842$	$1402524686897642881/20523074457600$	$0.96787$	$4.70694$	$[0, 0, 0, -13432332, -18707420144]$	$y^2=x^3-13432332x-18707420144$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.2, 24.48.0-8.d.2.6, 88.48.0.?, $\ldots$	$[ ]$
411840.km4	411840km2	411840.km	411840km	$6$	$8$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{30} \cdot 3^{10} \cdot 5^{2} \cdot 11^{4} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.13	2Cs	$17160$	$192$	$1$	$1$	$1$	$3$	$23592960$	$2.946842$	$1402524686897642881/20523074457600$	$0.96787$	$4.70694$	$[0, 0, 0, -13432332, 18707420144]$	$y^2=x^3-13432332x+18707420144$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.2, 24.48.0-8.d.2.5, 88.48.0.?, $\ldots$	$[ ]$
446160.be4	446160be2	446160.be	446160be	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 13^{2} $	$ 2^{24} \cdot 3^{4} \cdot 5^{2} \cdot 11^{4} \cdot 13^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.13	2Cs	$17160$	$192$	$1$	$4.442928964$	$1$	$5$	$61931520$	$3.333435$	$1402524686897642881/20523074457600$	$0.96787$	$5.03460$	$[0, -1, 0, -63057336, 190299732336]$	$y^2=x^3-x^2-63057336x+190299732336$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.2, 20.24.0-4.b.1.2, 40.48.0-8.d.2.15, $\ldots$	$[(546, 395010)]$

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (20 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 (20 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