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 (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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
2090.b3	2090e2	2090.b	2090e	$4$	$6$	$ 2 \cdot 5 \cdot 11 \cdot 19 $	$ - 2 \cdot 5 \cdot 11^{6} \cdot 19^{2} $	$1$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$25080$	$96$	$1$	$3.160099834$	$1$		$6$	$1728$	$0.585273$	$-11741970526489/6395335210$	$0.90056$	$4.02326$	$[1, 0, 1, -474, 5486]$	$y^2+xy+y=x^3-474x+5486$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 40.6.0.a.1, 120.48.0.?, $\ldots$	$[(16, 37)]$
10450.bg3	10450bb2	10450.bg	10450bb	$4$	$6$	$ 2 \cdot 5^{2} \cdot 11 \cdot 19 $	$ - 2 \cdot 5^{7} \cdot 11^{6} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$1$	$1$		$0$	$41472$	$1.389992$	$-11741970526489/6395335210$	$0.90056$	$4.36704$	$[1, 1, 1, -11838, 685781]$	$y^2+xy+y=x^3+x^2-11838x+685781$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 15.8.0-3.a.1.2, 24.24.0-6.a.1.12, $\ldots$	$[ ]$
16720.bh3	16720s2	16720.bh	16720s	$4$	$6$	$ 2^{4} \cdot 5 \cdot 11 \cdot 19 $	$ - 2^{13} \cdot 5 \cdot 11^{6} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$1$	$4$	$2$	$1$	$41472$	$1.278419$	$-11741970526489/6395335210$	$0.90056$	$4.01828$	$[0, -1, 0, -7576, -351120]$	$y^2=x^3-x^2-7576x-351120$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0-6.a.1.3, 40.6.0.a.1, $\ldots$	$[ ]$
18810.z3	18810be2	18810.z	18810be	$4$	$6$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 19 $	$ - 2 \cdot 3^{6} \cdot 5 \cdot 11^{6} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$25080$	$96$	$1$	$12.59888757$	$1$		$0$	$41472$	$1.134579$	$-11741970526489/6395335210$	$0.90056$	$3.79482$	$[1, -1, 1, -4262, -148129]$	$y^2+xy+y=x^3-x^2-4262x-148129$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 40.6.0.a.1, 120.48.0.?, $\ldots$	$[(244189/36, 107081659/36)]$
22990.x3	22990v2	22990.x	22990v	$4$	$6$	$ 2 \cdot 5 \cdot 11^{2} \cdot 19 $	$ - 2 \cdot 5 \cdot 11^{12} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$19.28609214$	$1$		$0$	$207360$	$1.784222$	$-11741970526489/6395335210$	$0.90056$	$4.49524$	$[1, 0, 0, -57296, -7359494]$	$y^2+xy=x^3-57296x-7359494$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 33.8.0-3.a.1.2, 40.6.0.a.1, $\ldots$	$[(221357397/332, 3231850505545/332)]$
39710.ba3	39710x2	39710.ba	39710x	$4$	$6$	$ 2 \cdot 5 \cdot 11 \cdot 19^{2} $	$ - 2 \cdot 5 \cdot 11^{6} \cdot 19^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$1$	$4$	$2$	$0$	$622080$	$2.057491$	$-11741970526489/6395335210$	$0.90056$	$4.57290$	$[1, 1, 1, -170941, -37972067]$	$y^2+xy+y=x^3+x^2-170941x-37972067$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 40.6.0.a.1, 57.8.0-3.a.1.1, $\ldots$	$[ ]$
66880.bc3	66880dw2	66880.bc	66880dw	$4$	$6$	$ 2^{6} \cdot 5 \cdot 11 \cdot 19 $	$ - 2^{19} \cdot 5 \cdot 11^{6} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$5.081482421$	$1$		$5$	$331776$	$1.624994$	$-11741970526489/6395335210$	$0.90056$	$3.89123$	$[0, 1, 0, -30305, -2839265]$	$y^2=x^3+x^2-30305x-2839265$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 24.24.0-6.a.1.6, 30.24.0-6.a.1.3, $\ldots$	$[(213, 644)]$
66880.dd3	66880y2	66880.dd	66880y	$4$	$6$	$ 2^{6} \cdot 5 \cdot 11 \cdot 19 $	$ - 2^{19} \cdot 5 \cdot 11^{6} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$1$	$1$		$1$	$331776$	$1.624994$	$-11741970526489/6395335210$	$0.90056$	$3.89123$	$[0, -1, 0, -30305, 2839265]$	$y^2=x^3-x^2-30305x+2839265$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 24.24.0-6.a.1.11, 40.6.0.a.1, $\ldots$	$[ ]$
83600.c3	83600bi2	83600.c	83600bi	$4$	$6$	$ 2^{4} \cdot 5^{2} \cdot 11 \cdot 19 $	$ - 2^{13} \cdot 5^{7} \cdot 11^{6} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$1$	$1$		$1$	$995328$	$2.083138$	$-11741970526489/6395335210$	$0.90056$	$4.29969$	$[0, 1, 0, -189408, -44268812]$	$y^2=x^3+x^2-189408x-44268812$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 24.24.0-6.a.1.5, 40.6.0.a.1, $\ldots$	$[ ]$
94050.cb3	94050v2	94050.cb	94050v	$4$	$6$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 19 $	$ - 2 \cdot 3^{6} \cdot 5^{7} \cdot 11^{6} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$10.98716339$	$1$		$0$	$995328$	$1.939299$	$-11741970526489/6395335210$	$0.90056$	$4.10474$	$[1, -1, 0, -106542, -18622634]$	$y^2+xy=x^3-x^2-106542x-18622634$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 15.8.0-3.a.1.1, 24.24.0-6.a.1.4, $\ldots$	$[(279319/9, 145652327/9)]$
102410.bb3	102410x2	102410.bb	102410x	$4$	$6$	$ 2 \cdot 5 \cdot 7^{2} \cdot 11 \cdot 19 $	$ - 2 \cdot 5 \cdot 7^{6} \cdot 11^{6} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$175560$	$96$	$1$	$1$	$1$		$0$	$497664$	$1.558228$	$-11741970526489/6395335210$	$0.90056$	$3.67807$	$[1, 1, 0, -23202, -1904986]$	$y^2+xy=x^3+x^2-23202x-1904986$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 21.8.0-3.a.1.1, 40.6.0.a.1, $\ldots$	$[ ]$
114950.bk3	114950q2	114950.bk	114950q	$4$	$6$	$ 2 \cdot 5^{2} \cdot 11^{2} \cdot 19 $	$ - 2 \cdot 5^{7} \cdot 11^{12} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$1$	$1$		$0$	$4976640$	$2.588940$	$-11741970526489/6395335210$	$0.90056$	$4.70308$	$[1, 1, 0, -1432400, -919936750]$	$y^2+xy=x^3+x^2-1432400x-919936750$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 40.6.0.a.1, 120.24.0.?, $\ldots$	$[ ]$
150480.eh3	150480be2	150480.eh	150480be	$4$	$6$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 19 $	$ - 2^{13} \cdot 3^{6} \cdot 5 \cdot 11^{6} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$2.407741126$	$1$		$3$	$995328$	$1.827726$	$-11741970526489/6395335210$	$0.90056$	$3.83061$	$[0, 0, 0, -68187, 9548426]$	$y^2=x^3-68187x+9548426$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0-6.a.1.9, 40.6.0.a.1, $\ldots$	$[(170, 1694)]$
183920.cg3	183920bn2	183920.cg	183920bn	$4$	$6$	$ 2^{4} \cdot 5 \cdot 11^{2} \cdot 19 $	$ - 2^{13} \cdot 5 \cdot 11^{12} \cdot 19^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$20.59302945$	$1$		$3$	$4976640$	$2.477367$	$-11741970526489/6395335210$	$0.90056$	$4.41029$	$[0, -1, 0, -916736, 471007616]$	$y^2=x^3-x^2-916736x+471007616$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 40.6.0.a.1, 120.24.0.?, $\ldots$	$[(730, 13794), (220642/23, 154396242/23)]$
198550.j3	198550ca2	198550.j	198550ca	$4$	$6$	$ 2 \cdot 5^{2} \cdot 11 \cdot 19^{2} $	$ - 2 \cdot 5^{7} \cdot 11^{6} \cdot 19^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$3.809953137$	$1$		$2$	$14929920$	$2.862213$	$-11741970526489/6395335210$	$0.90056$	$4.76119$	$[1, 0, 1, -4273526, -4737961302]$	$y^2+xy+y=x^3-4273526x-4737961302$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 40.6.0.a.1, 120.24.0.?, $\ldots$	$[(5046, 317142)]$
206910.cq3	206910dq2	206910.cq	206910dq	$4$	$6$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 19 $	$ - 2 \cdot 3^{6} \cdot 5 \cdot 11^{12} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$1$	$4$	$2$	$0$	$4976640$	$2.333527$	$-11741970526489/6395335210$	$0.90056$	$4.22683$	$[1, -1, 0, -515664, 198706338]$	$y^2+xy=x^3-x^2-515664x+198706338$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 33.8.0-3.a.1.1, 40.6.0.a.1, $\ldots$	$[ ]$
317680.o3	317680o2	317680.o	317680o	$4$	$6$	$ 2^{4} \cdot 5 \cdot 11 \cdot 19^{2} $	$ - 2^{13} \cdot 5 \cdot 11^{6} \cdot 19^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$8.911213985$	$1$		$1$	$14929920$	$2.750641$	$-11741970526489/6395335210$	$0.90056$	$4.47887$	$[0, 1, 0, -2735056, 2424742164]$	$y^2=x^3+x^2-2735056x+2424742164$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 40.6.0.a.1, 120.24.0.?, $\ldots$	$[(5269/2, 266455/2)]$
334400.bl3	334400bl2	334400.bl	334400bl	$4$	$6$	$ 2^{6} \cdot 5^{2} \cdot 11 \cdot 19 $	$ - 2^{19} \cdot 5^{7} \cdot 11^{6} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$8.098023622$	$1$		$1$	$7962624$	$2.429714$	$-11741970526489/6395335210$	$0.90056$	$4.15805$	$[0, 1, 0, -757633, 353392863]$	$y^2=x^3+x^2-757633x+353392863$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0-6.a.1.10, 40.6.0.a.1, $\ldots$	$[(30577/3, 5194000/3)]$
334400.ft3	334400ft2	334400.ft	334400ft	$4$	$6$	$ 2^{6} \cdot 5^{2} \cdot 11 \cdot 19 $	$ - 2^{19} \cdot 5^{7} \cdot 11^{6} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$1$	$1$		$1$	$7962624$	$2.429714$	$-11741970526489/6395335210$	$0.90056$	$4.15805$	$[0, -1, 0, -757633, -353392863]$	$y^2=x^3-x^2-757633x-353392863$	2.3.0.a.1, 3.4.0.a.1, 6.24.0-6.a.1.1, 40.6.0.a.1, 120.48.0.?, $\ldots$	$[ ]$
353210.bi3	353210bi2	353210.bi	353210bi	$4$	$6$	$ 2 \cdot 5 \cdot 11 \cdot 13^{2} \cdot 19 $	$ - 2 \cdot 5 \cdot 11^{6} \cdot 13^{6} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$326040$	$96$	$1$	$8.179332675$	$1$		$0$	$3981312$	$1.867748$	$-11741970526489/6395335210$	$0.90056$	$3.61235$	$[1, 0, 0, -80025, 12133315]$	$y^2+xy=x^3-80025x+12133315$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 39.8.0-3.a.1.1, 40.6.0.a.1, $\ldots$	$[(-23209/10, 4384309/10)]$
357390.bd3	357390bd2	357390.bd	357390bd	$4$	$6$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 19^{2} $	$ - 2 \cdot 3^{6} \cdot 5 \cdot 11^{6} \cdot 19^{8} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$16.12997868$	$1$		$4$	$14929920$	$2.606800$	$-11741970526489/6395335210$	$0.90056$	$4.30262$	$[1, -1, 0, -1538469, 1023707335]$	$y^2+xy=x^3-x^2-1538469x+1023707335$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 40.6.0.a.1, 57.8.0-3.a.1.2, $\ldots$	$[(765, 16765), (34321/3, 6022163/3)]$
436810.bh3	436810bh2	436810.bh	436810bh	$4$	$6$	$ 2 \cdot 5 \cdot 11^{2} \cdot 19^{2} $	$ - 2 \cdot 5 \cdot 11^{12} \cdot 19^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$25080$	$96$	$1$	$33.17283460$	$1$		$0$	$74649600$	$3.256439$	$-11741970526489/6395335210$	$0.90056$	$4.83639$	$[1, 1, 0, -20683863, 50437401623]$	$y^2+xy=x^3+x^2-20683863x+50437401623$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0-6.a.1.11, 40.6.0.a.1, $\ldots$	$[(-157783590905171/177708, 971182726674465982117/177708)]$

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 (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