LMFDB - Elliptic curves over $\Q$ of conductor 550

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 (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
550.a1	550d2	550.a	550d	$2$	$3$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2^{3} \cdot 5^{8} \cdot 11^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$264$	$16$	$0$	$1$	$1$	$0$	$540$	$0.568795$	$-53969305/10648$	$0.89387$	$4.90859$	$[1, 0, 1, -576, -6202]$	$y^2+xy+y=x^3-576x-6202$	3.8.0-3.a.1.1, 88.2.0.?, 264.16.0.?	$[]$
550.a2	550d1	550.a	550d	$2$	$3$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2 \cdot 5^{8} \cdot 11 $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$264$	$16$	$0$	$1$	$1$	$2$	$180$	$0.019489$	$34295/22$	$0.82040$	$3.69549$	$[1, 0, 1, 49, 48]$	$y^2+xy+y=x^3+49x+48$	3.8.0-3.a.1.2, 88.2.0.?, 264.16.0.?	$[]$
550.b1	550c1	550.b	550c	$1$	$1$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2^{11} \cdot 5^{2} \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$88$	$2$	$0$	$1$	$1$	$0$	$132$	$0.048433$	$-38401771585/22528$	$0.95307$	$4.37268$	$[1, 0, 1, -206, -1152]$	$y^2+xy+y=x^3-206x-1152$	88.2.0.?	$[]$
550.c1	550g2	550.c	550g	$2$	$2$	$ 2 \cdot 5^{2} \cdot 11 $	$ 2^{2} \cdot 5^{3} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$0.174018903$	$1$	$14$	$96$	$-0.126250$	$1039509197/484$	$0.93121$	$4.05557$	$[1, 0, 1, -106, 408]$	$y^2+xy+y=x^3-106x+408$	2.3.0.a.1, 10.6.0.a.1, 44.6.0.d.1, 220.12.0.?	$[(3, 9)]$
550.c2	550g1	550.c	550g	$2$	$2$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2^{4} \cdot 5^{3} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$0.348037806$	$1$	$9$	$48$	$-0.472824$	$-148877/176$	$0.84151$	$2.82919$	$[1, 0, 1, -6, 8]$	$y^2+xy+y=x^3-6x+8$	2.3.0.a.1, 20.6.0.c.1, 44.6.0.d.1, 110.6.0.?, 220.12.0.?	$[(1, 1)]$
550.d1	550a1	550.d	550a	$2$	$3$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2^{3} \cdot 5^{7} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1320$	$16$	$0$	$0.165868134$	$1$	$6$	$96$	$-0.002387$	$-117649/440$	$0.93815$	$3.69925$	$[1, 1, 0, -25, 125]$	$y^2+xy=x^3+x^2-25x+125$	3.4.0.a.1, 15.8.0-3.a.1.2, 264.8.0.?, 440.2.0.?, 1320.16.0.?	$[(5, 10)]$
550.d2	550a2	550.d	550a	$2$	$3$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2 \cdot 5^{9} \cdot 11^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1320$	$16$	$0$	$0.497604403$	$1$	$4$	$288$	$0.546920$	$80062991/332750$	$0.92204$	$4.70316$	$[1, 1, 0, 225, -3125]$	$y^2+xy=x^3+x^2+225x-3125$	3.4.0.a.1, 15.8.0-3.a.1.1, 264.8.0.?, 440.2.0.?, 1320.16.0.?	$[(15, 55)]$
550.e1	550f3	550.e	550f	$3$	$25$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2^{25} \cdot 5^{9} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.120.0.2	5B.1.4	$2200$	$1200$	$37$	$1.796003113$	$1$	$4$	$6000$	$1.987846$	$-24680042791780949/369098752$	$1.03557$	$8.27740$	$[1, 0, 1, -758201, 254051548]$	$y^2+xy+y=x^3-758201x+254051548$	5.24.0-5.a.1.1, 25.120.0-25.a.1.1, 275.600.12.?, 440.48.1.?, 2200.1200.37.?	$[(502, -189)]$
550.e2	550f1	550.e	550f	$3$	$25$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2 \cdot 5^{9} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.120.0.4	5B.1.3	$2200$	$1200$	$37$	$1.796003113$	$1$	$2$	$240$	$0.378409$	$-19465109/22$	$1.06489$	$4.95585$	$[1, 0, 1, -701, -7202]$	$y^2+xy+y=x^3-701x-7202$	5.24.0-5.a.2.1, 25.120.0-25.a.2.1, 275.600.12.?, 440.48.1.?, 2200.1200.37.?	$[(52, 286)]$
550.e3	550f2	550.e	550f	$3$	$25$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2^{5} \cdot 5^{9} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.120.0.2	5Cs.1.3	$2200$	$1200$	$37$	$0.359200622$	$1$	$6$	$1200$	$1.183128$	$6761990971/5153632$	$1.05709$	$5.88273$	$[1, 0, 1, 4924, 75298]$	$y^2+xy+y=x^3+4924x+75298$	5.120.0-5.a.1.1, 275.600.12.?, 440.240.5.?, 2200.1200.37.?	$[(52, 661)]$
550.f1	550b2	550.f	550b	$2$	$5$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2 \cdot 5^{7} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.24.0.4	5B.1.3	$440$	$48$	$1$	$1$	$1$	$0$	$2400$	$1.449795$	$-23178622194826561/1610510$	$1.01294$	$7.50226$	$[1, 0, 1, -148501, -22038602]$	$y^2+xy+y=x^3-148501x-22038602$	5.24.0-5.a.2.1, 440.48.1.?	$[]$
550.f2	550b1	550.f	550b	$2$	$5$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2^{5} \cdot 5^{11} \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.24.0.2	5B.1.4	$440$	$48$	$1$	$1$	$1$	$0$	$480$	$0.645076$	$109902239/1100000$	$0.94438$	$4.90697$	$[1, 0, 1, 249, -6102]$	$y^2+xy+y=x^3+249x-6102$	5.24.0-5.a.1.1, 440.48.1.?	$[]$
550.g1	550e1	550.g	550e	$1$	$1$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2^{11} \cdot 5^{9} \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$440$	$2$	$0$	$1$	$1$	$0$	$880$	$0.725106$	$-2803221/22528$	$0.99503$	$5.07641$	$[1, -1, 0, -367, 10541]$	$y^2+xy=x^3-x^2-367x+10541$	440.2.0.?	$[]$
550.h1	550j1	550.h	550j	$1$	$1$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2^{11} \cdot 5^{3} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$440$	$2$	$0$	$0.039906259$	$1$	$14$	$176$	$-0.079613$	$-2803221/22528$	$0.99503$	$3.54602$	$[1, -1, 1, -15, 87]$	$y^2+xy+y=x^3-x^2-15x+87$	440.2.0.?	$[(-1, 10)]$
550.i1	550i1	550.i	550i	$2$	$3$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2^{7} \cdot 5^{7} \cdot 11^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1320$	$16$	$0$	$0.021400148$	$1$	$18$	$672$	$0.757527$	$-76711450249/851840$	$0.93960$	$5.50545$	$[1, 1, 1, -2213, 39531]$	$y^2+xy+y=x^3+x^2-2213x+39531$	3.4.0.a.1, 15.8.0-3.a.1.2, 264.8.0.?, 440.2.0.?, 1320.16.0.?	$[(-35, 292)]$
550.i2	550i2	550.i	550i	$2$	$3$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2^{21} \cdot 5^{9} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1320$	$16$	$0$	$0.064200444$	$1$	$12$	$2016$	$1.306833$	$2882081488391/2883584000$	$0.98944$	$6.07712$	$[1, 1, 1, 7412, 212781]$	$y^2+xy+y=x^3+x^2+7412x+212781$	3.4.0.a.1, 15.8.0-3.a.1.1, 264.8.0.?, 440.2.0.?, 1320.16.0.?	$[(5, 497)]$
550.j1	550k3	550.j	550k	$3$	$25$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2^{25} \cdot 5^{3} \cdot 11 $	$0$	$\Z/5\Z$	$\Q$	$\mathrm{SU}(2)$	$5$	25.120.0.1	5B.1.1	$2200$	$1200$	$37$	$1$	$1$	$4$	$1200$	$1.183128$	$-24680042791780949/369098752$	$1.03557$	$6.74701$	$[1, 1, 1, -30328, 2020281]$	$y^2+xy+y=x^3+x^2-30328x+2020281$	5.24.0-5.a.1.2, 25.120.0-25.a.1.2, 275.600.12.?, 440.48.1.?, 2200.1200.37.?	$[]$
550.j2	550k1	550.j	550k	$3$	$25$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2 \cdot 5^{3} \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.120.0.3	5B.1.2	$2200$	$1200$	$37$	$1$	$1$	$0$	$48$	$-0.426310$	$-19465109/22$	$1.06489$	$3.42546$	$[1, 1, 1, -28, -69]$	$y^2+xy+y=x^3+x^2-28x-69$	5.24.0-5.a.2.2, 25.120.0-25.a.2.2, 275.600.12.?, 440.48.1.?, 2200.1200.37.?	$[]$
550.j3	550k2	550.j	550k	$3$	$25$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2^{5} \cdot 5^{3} \cdot 11^{5} $	$0$	$\Z/5\Z$	$\Q$	$\mathrm{SU}(2)$	$5$	5.120.0.1	5Cs.1.1	$2200$	$1200$	$37$	$1$	$1$	$4$	$240$	$0.378409$	$6761990971/5153632$	$1.05709$	$4.35234$	$[1, 1, 1, 197, 681]$	$y^2+xy+y=x^3+x^2+197x+681$	5.120.0-5.a.1.2, 275.600.12.?, 440.240.5.?, 2200.1200.37.?	$[]$
550.k1	550l2	550.k	550l	$2$	$2$	$ 2 \cdot 5^{2} \cdot 11 $	$ 2^{2} \cdot 5^{9} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$1$	$1$	$0$	$480$	$0.678469$	$1039509197/484$	$0.93121$	$5.58596$	$[1, 1, 1, -2638, 51031]$	$y^2+xy+y=x^3+x^2-2638x+51031$	2.3.0.a.1, 10.6.0.a.1, 44.6.0.d.1, 220.12.0.?	$[]$
550.k2	550l1	550.k	550l	$2$	$2$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2^{4} \cdot 5^{9} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$1$	$1$	$1$	$240$	$0.331895$	$-148877/176$	$0.84151$	$4.35958$	$[1, 1, 1, -138, 1031]$	$y^2+xy+y=x^3+x^2-138x+1031$	2.3.0.a.1, 20.6.0.c.1, 44.6.0.d.1, 110.6.0.?, 220.12.0.?	$[]$
550.l1	550m1	550.l	550m	$1$	$1$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2^{11} \cdot 5^{8} \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$88$	$2$	$0$	$1$	$1$	$0$	$660$	$0.853152$	$-38401771585/22528$	$0.95307$	$5.90307$	$[1, 1, 1, -5138, -143969]$	$y^2+xy+y=x^3+x^2-5138x-143969$	88.2.0.?	$[]$
550.m1	550h2	550.m	550h	$2$	$3$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2^{3} \cdot 5^{2} \cdot 11^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1320$	$16$	$0$	$1$	$1$	$0$	$108$	$-0.235924$	$-53969305/10648$	$0.89387$	$3.37820$	$[1, 1, 1, -23, -59]$	$y^2+xy+y=x^3+x^2-23x-59$	3.4.0.a.1, 15.8.0-3.a.1.1, 88.2.0.?, 264.8.0.?, 1320.16.0.?	$[]$
550.m2	550h1	550.m	550h	$2$	$3$	$ 2 \cdot 5^{2} \cdot 11 $	$ - 2 \cdot 5^{2} \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1320$	$16$	$0$	$1$	$1$	$0$	$36$	$-0.785230$	$34295/22$	$0.82040$	$2.16510$	$[1, 1, 1, 2, 1]$	$y^2+xy+y=x^3+x^2+2x+1$	3.4.0.a.1, 15.8.0-3.a.1.2, 88.2.0.?, 264.8.0.?, 1320.16.0.?	$[]$

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 $\F_{q}$

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