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	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
9240.d2	9240a2	9240.d	9240a	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$3080$	$48$	$0$	$1$	$1$	$3$	$8192$	$0.732855$	$690862540036/12006225$	$0.88334$	$3.74456$	$[0, -1, 0, -1856, -29700]$	$y^2=x^3-x^2-1856x-29700$	2.6.0.a.1, 8.12.0-2.a.1.1, 20.12.0-2.a.1.1, 40.24.0-40.b.1.3, 308.12.0.?, $\ldots$	$[ ]$
18480.bz2	18480u2	18480.bz	18480u	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$3080$	$48$	$0$	$0.532246555$	$1$	$17$	$16384$	$0.732855$	$690862540036/12006225$	$0.88334$	$3.48037$	$[0, 1, 0, -1856, 29700]$	$y^2=x^3+x^2-1856x+29700$	2.6.0.a.1, 8.12.0-2.a.1.1, 20.12.0-2.a.1.1, 40.24.0-40.b.1.2, 308.12.0.?, $\ldots$	$[(34, 84)]$
27720.bs2	27720br2	27720.bs	27720br	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{10} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$1$	$1$	$3$	$65536$	$1.282162$	$690862540036/12006225$	$0.88334$	$3.98678$	$[0, 0, 0, -16707, 818606]$	$y^2=x^3-16707x+818606$	2.6.0.a.1, 24.12.0-2.a.1.1, 40.12.0.b.1, 60.12.0-2.a.1.1, 120.24.0.?, $\ldots$	$[ ]$
46200.by2	46200ck2	46200.by	46200ck	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{4} \cdot 5^{8} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$3080$	$48$	$0$	$2.721068711$	$1$	$9$	$196608$	$1.537575$	$690862540036/12006225$	$0.88334$	$4.08252$	$[0, 1, 0, -46408, -3805312]$	$y^2=x^3+x^2-46408x-3805312$	2.6.0.a.1, 4.12.0-2.a.1.1, 40.24.0-40.b.1.4, 616.24.0.?, 1540.24.0.?, $\ldots$	$[(-136, 96)]$
55440.dc2	55440bc2	55440.dc	55440bc	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{10} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$2.047102341$	$1$	$9$	$131072$	$1.282162$	$690862540036/12006225$	$0.88334$	$3.73379$	$[0, 0, 0, -16707, -818606]$	$y^2=x^3-16707x-818606$	2.6.0.a.1, 24.12.0-2.a.1.1, 40.12.0.b.1, 60.12.0-2.a.1.1, 120.24.0.?, $\ldots$	$[(-75, 112)]$
64680.da2	64680bd2	64680.da	64680bd	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 7^{8} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$3080$	$48$	$0$	$1$	$1$	$3$	$393216$	$1.705811$	$690862540036/12006225$	$0.88334$	$4.14077$	$[0, 1, 0, -90960, 10369008]$	$y^2=x^3+x^2-90960x+10369008$	2.6.0.a.1, 40.12.0.b.1, 44.12.0-2.a.1.1, 56.12.0-2.a.1.1, 140.12.0.?, $\ldots$	$[ ]$
73920.cf2	73920fi2	73920.cf	73920fi	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$3080$	$48$	$0$	$1.284303451$	$1$	$11$	$131072$	$1.079430$	$690862540036/12006225$	$0.88334$	$3.42097$	$[0, -1, 0, -7425, 245025]$	$y^2=x^3-x^2-7425x+245025$	2.6.0.a.1, 4.12.0-2.a.1.1, 40.24.0-40.b.1.4, 616.24.0.?, 1540.24.0.?, $\ldots$	$[(0, 495)]$
73920.ib2	73920dt2	73920.ib	73920dt	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$3080$	$48$	$0$	$2.139436654$	$1$	$9$	$131072$	$1.079430$	$690862540036/12006225$	$0.88334$	$3.42097$	$[0, 1, 0, -7425, -245025]$	$y^2=x^3+x^2-7425x-245025$	2.6.0.a.1, 4.12.0-2.a.1.1, 40.24.0-40.b.1.1, 616.24.0.?, 1540.24.0.?, $\ldots$	$[(-51, 60)]$
92400.di2	92400x2	92400.di	92400x	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{4} \cdot 5^{8} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$3080$	$48$	$0$	$1.398686007$	$1$	$13$	$393216$	$1.537575$	$690862540036/12006225$	$0.88334$	$3.83503$	$[0, -1, 0, -46408, 3805312]$	$y^2=x^3-x^2-46408x+3805312$	2.6.0.a.1, 4.12.0-2.a.1.1, 40.24.0-40.b.1.1, 616.24.0.?, 1540.24.0.?, $\ldots$	$[(148, 396)]$
101640.d2	101640bs2	101640.d	101640bs	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} $	$ 2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$3080$	$48$	$0$	$3.048797353$	$1$	$7$	$983040$	$1.931803$	$690862540036/12006225$	$0.88334$	$4.21366$	$[0, -1, 0, -224616, 40429116]$	$y^2=x^3-x^2-224616x+40429116$	2.6.0.a.1, 28.12.0-2.a.1.1, 40.12.0.b.1, 88.12.0.?, 220.12.0.?, $\ldots$	$[(-42, 7056)]$
129360.dl2	129360bq2	129360.dl	129360bq	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 7^{8} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$3080$	$48$	$0$	$1$	$1$	$3$	$786432$	$1.705811$	$690862540036/12006225$	$0.88334$	$3.89692$	$[0, -1, 0, -90960, -10369008]$	$y^2=x^3-x^2-90960x-10369008$	2.6.0.a.1, 40.12.0.b.1, 44.12.0-2.a.1.1, 56.12.0-2.a.1.1, 140.12.0.?, $\ldots$	$[ ]$
138600.bq2	138600dz2	138600.bq	138600dz	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{10} \cdot 5^{8} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$2.413369577$	$1$	$9$	$1572864$	$2.086880$	$690862540036/12006225$	$0.88334$	$4.26045$	$[0, 0, 0, -417675, 102325750]$	$y^2=x^3-417675x+102325750$	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0.b.1, 120.24.0.?, 616.12.0.?, $\ldots$	$[(311, 1584)]$
194040.bo2	194040y2	194040.bo	194040y	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{10} \cdot 3^{10} \cdot 5^{2} \cdot 7^{8} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$3.857064992$	$1$	$7$	$3145728$	$2.255116$	$690862540036/12006225$	$0.88334$	$4.30852$	$[0, 0, 0, -818643, -280781858]$	$y^2=x^3-818643x-280781858$	2.6.0.a.1, 40.12.0.b.1, 132.12.0.?, 168.12.0.?, 420.12.0.?, $\ldots$	$[(-493, 1728)]$
203280.ey2	203280fq2	203280.ey	203280fq	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} $	$ 2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$3080$	$48$	$0$	$1$	$1$	$3$	$1966080$	$1.931803$	$690862540036/12006225$	$0.88334$	$3.97469$	$[0, 1, 0, -224616, -40429116]$	$y^2=x^3+x^2-224616x-40429116$	2.6.0.a.1, 28.12.0-2.a.1.1, 40.12.0.b.1, 88.12.0.?, 220.12.0.?, $\ldots$	$[ ]$
221760.ck2	221760er2	221760.ck	221760er	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{10} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$1$	$1$	$3$	$1048576$	$1.628735$	$690862540036/12006225$	$0.88334$	$3.65115$	$[0, 0, 0, -66828, -6548848]$	$y^2=x^3-66828x-6548848$	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0.b.1, 120.24.0.?, 616.12.0.?, $\ldots$	$[ ]$
221760.dw2	221760kx2	221760.dw	221760kx	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{10} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$1.539471104$	$1$	$13$	$1048576$	$1.628735$	$690862540036/12006225$	$0.88334$	$3.65115$	$[0, 0, 0, -66828, 6548848]$	$y^2=x^3-66828x+6548848$	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0.b.1, 120.24.0.?, 616.12.0.?, $\ldots$	$[(38, 2016)]$
277200.hz2	277200hz2	277200.hz	277200hz	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{10} \cdot 5^{8} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$1.812114515$	$1$	$13$	$3145728$	$2.086880$	$690862540036/12006225$	$0.88334$	$4.02482$	$[0, 0, 0, -417675, -102325750]$	$y^2=x^3-417675x-102325750$	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0.b.1, 120.24.0.?, 616.12.0.?, $\ldots$	$[(-389, 1134)]$
304920.cy2	304920cy2	304920.cy	304920cy	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} $	$ 2^{10} \cdot 3^{10} \cdot 5^{2} \cdot 7^{2} \cdot 11^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$1$	$1$	$3$	$7864320$	$2.481110$	$690862540036/12006225$	$0.88334$	$4.36907$	$[0, 0, 0, -2021547, -1089564586]$	$y^2=x^3-2021547x-1089564586$	2.6.0.a.1, 40.12.0.b.1, 84.12.0.?, 264.12.0.?, 616.12.0.?, $\ldots$	$[ ]$
323400.bf2	323400bf2	323400.bf	323400bf	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ 2^{10} \cdot 3^{4} \cdot 5^{8} \cdot 7^{8} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$3080$	$48$	$0$	$2.672843821$	$1$	$9$	$9437184$	$2.510529$	$690862540036/12006225$	$0.88334$	$4.37663$	$[0, -1, 0, -2274008, 1300674012]$	$y^2=x^3-x^2-2274008x+1300674012$	2.6.0.a.1, 28.12.0-2.a.1.1, 40.12.0.b.1, 88.12.0.?, 220.12.0.?, $\ldots$	$[(737, 4950)]$
369600.fj2	369600fj2	369600.fj	369600fj	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{4} \cdot 5^{8} \cdot 7^{2} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$3080$	$48$	$0$	$1$	$1$	$3$	$3145728$	$1.884148$	$690862540036/12006225$	$0.88334$	$3.74474$	$[0, -1, 0, -185633, -30256863]$	$y^2=x^3-x^2-185633x-30256863$	2.6.0.a.1, 8.12.0-2.a.1.1, 20.12.0-2.a.1.1, 40.24.0-40.b.1.2, 308.12.0.?, $\ldots$	$[ ]$
369600.td2	369600td2	369600.td	369600td	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{4} \cdot 5^{8} \cdot 7^{2} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$3080$	$48$	$0$	$1$	$1$	$3$	$3145728$	$1.884148$	$690862540036/12006225$	$0.88334$	$3.74474$	$[0, 1, 0, -185633, 30256863]$	$y^2=x^3+x^2-185633x+30256863$	2.6.0.a.1, 8.12.0-2.a.1.1, 20.12.0-2.a.1.1, 40.24.0-40.b.1.3, 308.12.0.?, $\ldots$	$[ ]$
388080.bb2	388080bb2	388080.bb	388080bb	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{10} \cdot 3^{10} \cdot 5^{2} \cdot 7^{8} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$1.555137396$	$1$	$13$	$6291456$	$2.255116$	$690862540036/12006225$	$0.88334$	$4.07646$	$[0, 0, 0, -818643, 280781858]$	$y^2=x^3-818643x+280781858$	2.6.0.a.1, 40.12.0.b.1, 132.12.0.?, 168.12.0.?, 420.12.0.?, $\ldots$	$[(739, 8910)]$

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