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 (24 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	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
5070.j1	5070i1	5070.j	5070i	$2$	$3$	$ 2 \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2 \cdot 3^{3} \cdot 5^{3} \cdot 13^{4} $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$120$	$16$	$0$	$1$	$1$	$2$	$3024$	$0.461392$	$-2365581049/6750$	$0.97050$	$3.73328$	$[1, 0, 1, -849, 9466]$	$y^2+xy+y=x^3-849x+9466$	3.8.0-3.a.1.2, 120.16.0.?	$[ ]$
5070.v1	5070u1	5070.v	5070u	$2$	$3$	$ 2 \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2 \cdot 3^{3} \cdot 5^{3} \cdot 13^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1$	$1$	$0$	$39312$	$1.743866$	$-2365581049/6750$	$0.97050$	$5.53724$	$[1, 0, 0, -143400, 20940750]$	$y^2+xy=x^3-143400x+20940750$	3.4.0.a.1, 39.8.0-3.a.1.1, 120.8.0.?, 1560.16.0.?	$[ ]$
15210.e1	15210j1	15210.e	15210j	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2 \cdot 3^{9} \cdot 5^{3} \cdot 13^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1$	$1$	$0$	$314496$	$2.293171$	$-2365581049/6750$	$0.97050$	$5.59003$	$[1, -1, 0, -1290600, -565400250]$	$y^2+xy=x^3-x^2-1290600x-565400250$	3.4.0.a.1, 39.8.0-3.a.1.2, 120.8.0.?, 1560.16.0.?	$[ ]$
15210.br1	15210bp1	15210.br	15210bp	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2 \cdot 3^{9} \cdot 5^{3} \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$120$	$16$	$0$	$1$	$1$	$0$	$24192$	$1.010698$	$-2365581049/6750$	$0.97050$	$3.99188$	$[1, -1, 1, -7637, -255589]$	$y^2+xy+y=x^3-x^2-7637x-255589$	3.8.0-3.a.1.1, 120.16.0.?	$[ ]$
25350.s1	25350d1	25350.s	25350d	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2 \cdot 3^{3} \cdot 5^{9} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$3.865096205$	$1$	$2$	$943488$	$2.548584$	$-2365581049/6750$	$0.97050$	$5.61068$	$[1, 1, 0, -3585000, 2617593750]$	$y^2+xy=x^3+x^2-3585000x+2617593750$	3.4.0.a.1, 120.8.0.?, 195.8.0.?, 312.8.0.?, 1560.16.0.?	$[(875, 11875)]$
25350.cb1	25350bz1	25350.cb	25350bz	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2 \cdot 3^{3} \cdot 5^{9} \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$1$	$1$	$0$	$72576$	$1.266111$	$-2365581049/6750$	$0.97050$	$4.09304$	$[1, 1, 1, -21213, 1183281]$	$y^2+xy+y=x^3+x^2-21213x+1183281$	3.4.0.a.1, 15.8.0-3.a.1.2, 24.8.0-3.a.1.5, 120.16.0.?	$[ ]$
40560.f1	40560bj1	40560.f	40560bj	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{13} \cdot 3^{3} \cdot 5^{3} \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$1$	$1$	$0$	$72576$	$1.154539$	$-2365581049/6750$	$0.97050$	$3.78555$	$[0, -1, 0, -13576, -605840]$	$y^2=x^3-x^2-13576x-605840$	3.4.0.a.1, 12.8.0-3.a.1.1, 120.16.0.?	$[ ]$
40560.bb1	40560bs1	40560.bb	40560bs	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{13} \cdot 3^{3} \cdot 5^{3} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$8.045549628$	$1$	$2$	$943488$	$2.437012$	$-2365581049/6750$	$0.97050$	$5.23597$	$[0, -1, 0, -2294400, -1340208000]$	$y^2=x^3-x^2-2294400x-1340208000$	3.4.0.a.1, 120.8.0.?, 156.8.0.?, 1560.16.0.?	$[(42520, 8762040)]$
76050.z1	76050bn1	76050.z	76050bn	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} $	$ - 2 \cdot 3^{9} \cdot 5^{9} \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$1$	$1$	$0$	$580608$	$1.815416$	$-2365581049/6750$	$0.97050$	$4.27944$	$[1, -1, 0, -190917, -32139509]$	$y^2+xy=x^3-x^2-190917x-32139509$	3.4.0.a.1, 15.8.0-3.a.1.1, 24.8.0-3.a.1.6, 120.16.0.?	$[ ]$
76050.fk1	76050el1	76050.fk	76050el	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} $	$ - 2 \cdot 3^{9} \cdot 5^{9} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$43.76893255$	$1$	$0$	$7547904$	$3.097893$	$-2365581049/6750$	$0.97050$	$5.64874$	$[1, -1, 1, -32265005, -70707296253]$	$y^2+xy+y=x^3-x^2-32265005x-70707296253$	3.4.0.a.1, 120.8.0.?, 195.8.0.?, 312.8.0.?, 1560.16.0.?	$[(258621810374509118309/165759476, 3065692170559276105875685237095/165759476)]$
121680.cc1	121680do1	121680.cc	121680do	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{13} \cdot 3^{9} \cdot 5^{3} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$6.785586506$	$1$	$0$	$7547904$	$2.986320$	$-2365581049/6750$	$0.97050$	$5.30766$	$[0, 0, 0, -20649603, 36206265602]$	$y^2=x^3-20649603x+36206265602$	3.4.0.a.1, 120.8.0.?, 156.8.0.?, 1560.16.0.?	$[(11281/2, 160191/2)]$
121680.dr1	121680ey1	121680.dr	121680ey	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{13} \cdot 3^{9} \cdot 5^{3} \cdot 13^{4} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$0.158902240$	$1$	$28$	$580608$	$1.703846$	$-2365581049/6750$	$0.97050$	$3.99333$	$[0, 0, 0, -122187, 16479866]$	$y^2=x^3-122187x+16479866$	3.4.0.a.1, 12.8.0-3.a.1.2, 120.16.0.?	$[(637, 14040), (793/2, 1755/2)]$
162240.j1	162240hs1	162240.j	162240hs	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{19} \cdot 3^{3} \cdot 5^{3} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$6.033479441$	$1$	$2$	$7547904$	$2.783588$	$-2365581049/6750$	$0.97050$	$4.97759$	$[0, -1, 0, -9177601, 10730841601]$	$y^2=x^3-x^2-9177601x+10730841601$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 390.8.0.?, 1560.16.0.?	$[(-1695, 146336)]$
162240.ds1	162240hh1	162240.ds	162240hh	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{19} \cdot 3^{3} \cdot 5^{3} \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$1$	$1$	$0$	$580608$	$1.501112$	$-2365581049/6750$	$0.97050$	$3.69478$	$[0, -1, 0, -54305, 4901025]$	$y^2=x^3-x^2-54305x+4901025$	3.4.0.a.1, 24.8.0-3.a.1.2, 30.8.0-3.a.1.2, 120.16.0.?	$[ ]$
162240.fw1	162240bt1	162240.fw	162240bt	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{19} \cdot 3^{3} \cdot 5^{3} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$19.71297238$	$1$	$0$	$7547904$	$2.783588$	$-2365581049/6750$	$0.97050$	$4.97759$	$[0, 1, 0, -9177601, -10730841601]$	$y^2=x^3+x^2-9177601x-10730841601$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 780.8.0.?, 1560.16.0.?	$[(3153835495/421, 174364342431072/421)]$
162240.gs1	162240e1	162240.gs	162240e	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{19} \cdot 3^{3} \cdot 5^{3} \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$1$	$1$	$0$	$580608$	$1.501112$	$-2365581049/6750$	$0.97050$	$3.69478$	$[0, 1, 0, -54305, -4901025]$	$y^2=x^3+x^2-54305x-4901025$	3.4.0.a.1, 24.8.0-3.a.1.4, 60.8.0-3.a.1.3, 120.16.0.?	$[ ]$
202800.gn1	202800bt1	202800.gn	202800bt	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{13} \cdot 3^{3} \cdot 5^{9} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$10.87281260$	$1$	$0$	$22643712$	$3.241734$	$-2365581049/6750$	$0.97050$	$5.33660$	$[0, 1, 0, -57360008, -167640720012]$	$y^2=x^3+x^2-57360008x-167640720012$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 780.8.0.?, 1560.16.0.?	$[(1553497/8, 1827664125/8)]$
202800.ji1	202800cs1	202800.ji	202800cs	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{13} \cdot 3^{3} \cdot 5^{9} \cdot 13^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$4.710048922$	$1$	$2$	$1741824$	$1.959257$	$-2365581049/6750$	$0.97050$	$4.07721$	$[0, 1, 0, -339408, -76408812]$	$y^2=x^3+x^2-339408x-76408812$	3.4.0.a.1, 24.8.0-3.a.1.7, 60.8.0-3.a.1.2, 120.16.0.?	$[(762, 10392)]$
248430.br1	248430br1	248430.br	248430br	$2$	$3$	$ 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13^{2} $	$ - 2 \cdot 3^{3} \cdot 5^{3} \cdot 7^{6} \cdot 13^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$840$	$16$	$0$	$3.412782892$	$1$	$2$	$1088640$	$1.434347$	$-2365581049/6750$	$0.97050$	$3.50356$	$[1, 1, 0, -41577, -3288501]$	$y^2+xy=x^3+x^2-41577x-3288501$	3.4.0.a.1, 21.8.0-3.a.1.1, 120.8.0.?, 840.16.0.?	$[(503, 9916)]$
248430.gi1	248430gi1	248430.gi	248430gi	$2$	$3$	$ 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13^{2} $	$ - 2 \cdot 3^{3} \cdot 5^{3} \cdot 7^{6} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$10920$	$16$	$0$	$111.2610210$	$1$	$0$	$14152320$	$2.716820$	$-2365581049/6750$	$0.97050$	$4.74238$	$[1, 1, 1, -7026601, -7189703851]$	$y^2+xy+y=x^3+x^2-7026601x-7189703851$	3.4.0.a.1, 120.8.0.?, 273.8.0.?, 10920.16.0.?	$[(14291271778658027808365985862050064573721260643851/14798773595354855698294, 53875913392201406690735168092773709691100735335079997281458579246252994595/14798773595354855698294)]$
486720.co1	486720co1	486720.co	486720co	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{19} \cdot 3^{9} \cdot 5^{3} \cdot 13^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$2.244343760$	$1$	$2$	$4644864$	$2.050419$	$-2365581049/6750$	$0.97050$	$3.88817$	$[0, 0, 0, -488748, 131838928]$	$y^2=x^3-488748x+131838928$	3.4.0.a.1, 24.8.0-3.a.1.3, 60.8.0-3.a.1.4, 120.16.0.?	$[(458, 2016)]$
486720.fx1	486720fx1	486720.fx	486720fx	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{19} \cdot 3^{9} \cdot 5^{3} \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$1$	$1$	$0$	$4644864$	$2.050419$	$-2365581049/6750$	$0.97050$	$3.88817$	$[0, 0, 0, -488748, -131838928]$	$y^2=x^3-488748x-131838928$	3.4.0.a.1, 24.8.0-3.a.1.1, 30.8.0-3.a.1.1, 120.16.0.?	$[ ]$
486720.kx1	486720kx1	486720.kx	486720kx	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{19} \cdot 3^{9} \cdot 5^{3} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$12.46116412$	$1$	$0$	$60383232$	$3.332893$	$-2365581049/6750$	$0.97050$	$5.06337$	$[0, 0, 0, -82598412, -289650124816]$	$y^2=x^3-82598412x-289650124816$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 390.8.0.?, 1560.16.0.?	$[(7545352/23, 14570156340/23)]$
486720.om1	486720om1	486720.om	486720om	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{19} \cdot 3^{9} \cdot 5^{3} \cdot 13^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1$	$1$	$0$	$60383232$	$3.332893$	$-2365581049/6750$	$0.97050$	$5.06337$	$[0, 0, 0, -82598412, 289650124816]$	$y^2=x^3-82598412x+289650124816$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 780.8.0.?, 1560.16.0.?	$[ ]$

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 (24 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 (24 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