LMFDB - Elliptic curves over $\Q$ of conductor 880

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 (25 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
880.a1	880d1	880.a	880d	$1$	$1$	$ 2^{4} \cdot 5 \cdot 11 $	$ - 2^{11} \cdot 5^{3} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$440$	$2$	$0$	$0.054095025$	$1$	$12$	$288$	$-0.017441$	$-16241202/1375$	$0.86555$	$3.59358$	$[0, 0, 0, -67, 226]$	$y^2=x^3-67x+226$	440.2.0.?	$[(-3, 20)]$
880.b1	880h2	880.b	880h	$2$	$2$	$ 2^{4} \cdot 5 \cdot 11 $	$ 2^{8} \cdot 5^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$2.181749313$	$1$	$3$	$96$	$-0.199074$	$94875856/275$	$0.82986$	$3.52707$	$[0, 1, 0, -60, -200]$	$y^2=x^3+x^2-60x-200$	2.3.0.a.1, 20.6.0.c.1, 44.6.0.a.1, 220.12.0.?	$[(15, 50)]$
880.b2	880h1	880.b	880h	$2$	$2$	$ 2^{4} \cdot 5 \cdot 11 $	$ 2^{4} \cdot 5 \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$1.090874656$	$1$	$3$	$48$	$-0.545648$	$1048576/605$	$1.25294$	$2.45365$	$[0, 1, 0, -5, -2]$	$y^2=x^3+x^2-5x-2$	2.3.0.a.1, 10.6.0.a.1, 44.6.0.b.1, 220.12.0.?	$[(-2, 2)]$
880.c1	880e1	880.c	880e	$2$	$3$	$ 2^{4} \cdot 5 \cdot 11 $	$ - 2^{19} \cdot 5 \cdot 11^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1320$	$16$	$0$	$1$	$1$	$0$	$672$	$0.645956$	$-76711450249/851840$	$0.93960$	$4.92632$	$[0, -1, 0, -1416, -20240]$	$y^2=x^3-x^2-1416x-20240$	3.4.0.a.1, 12.8.0-3.a.1.1, 440.2.0.?, 1320.16.0.?	$[ ]$
880.c2	880e2	880.c	880e	$2$	$3$	$ 2^{4} \cdot 5 \cdot 11 $	$ - 2^{33} \cdot 5^{3} \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1320$	$16$	$0$	$1$	$1$	$0$	$2016$	$1.195263$	$2882081488391/2883584000$	$0.98944$	$5.45837$	$[0, -1, 0, 4744, -108944]$	$y^2=x^3-x^2+4744x-108944$	3.4.0.a.1, 12.8.0-3.a.1.2, 440.2.0.?, 1320.16.0.?	$[ ]$
880.d1	880f1	880.d	880f	$2$	$3$	$ 2^{4} \cdot 5 \cdot 11 $	$ - 2^{15} \cdot 5 \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1320$	$16$	$0$	$0.461060840$	$1$	$6$	$96$	$-0.113958$	$-117649/440$	$0.93815$	$3.24534$	$[0, -1, 0, -16, -64]$	$y^2=x^3-x^2-16x-64$	3.4.0.a.1, 12.8.0-3.a.1.1, 440.2.0.?, 1320.16.0.?	$[(8, 16)]$
880.d2	880f2	880.d	880f	$2$	$3$	$ 2^{4} \cdot 5 \cdot 11 $	$ - 2^{13} \cdot 5^{3} \cdot 11^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1320$	$16$	$0$	$0.153686946$	$1$	$8$	$288$	$0.435348$	$80062991/332750$	$0.92204$	$4.17965$	$[0, -1, 0, 144, 1600]$	$y^2=x^3-x^2+144x+1600$	3.4.0.a.1, 12.8.0-3.a.1.2, 440.2.0.?, 1320.16.0.?	$[(16, 88)]$
880.e1	880a2	880.e	880a	$2$	$2$	$ 2^{4} \cdot 5 \cdot 11 $	$ 2^{8} \cdot 5 \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$0.724720517$	$1$	$5$	$64$	$-0.272069$	$5256144/605$	$0.79186$	$3.10034$	$[0, 0, 0, -23, 38]$	$y^2=x^3-23x+38$	2.3.0.a.1, 10.6.0.a.1, 44.6.0.c.1, 220.12.0.?	$[(1, 4)]$
880.e2	880a1	880.e	880a	$2$	$2$	$ 2^{4} \cdot 5 \cdot 11 $	$ - 2^{4} \cdot 5^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$1.449441034$	$1$	$3$	$32$	$-0.618643$	$55296/275$	$0.96856$	$2.31867$	$[0, 0, 0, 2, 3]$	$y^2=x^3+2x+3$	2.3.0.a.1, 20.6.0.c.1, 22.6.0.a.1, 220.12.0.?	$[(3, 6)]$
880.f1	880b1	880.f	880b	$2$	$2$	$ 2^{4} \cdot 5 \cdot 11 $	$ 2^{4} \cdot 5^{3} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$1$	$1$	$1$	$96$	$-0.200426$	$379275264/15125$	$1.01554$	$3.32251$	$[0, 0, 0, -38, 87]$	$y^2=x^3-38x+87$	2.3.0.a.1, 10.6.0.a.1, 44.6.0.c.1, 220.12.0.?	$[ ]$
880.f2	880b2	880.f	880b	$2$	$2$	$ 2^{4} \cdot 5 \cdot 11 $	$ - 2^{8} \cdot 5^{6} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$1$	$1$	$1$	$192$	$0.146147$	$2122416/171875$	$1.06651$	$3.69433$	$[0, 0, 0, 17, 318]$	$y^2=x^3+17x+318$	2.3.0.a.1, 20.6.0.c.1, 22.6.0.a.1, 220.12.0.?	$[ ]$
880.g1	880c3	880.g	880c	$4$	$4$	$ 2^{4} \cdot 5 \cdot 11 $	$ 2^{10} \cdot 5^{3} \cdot 11^{8} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.47	2B	$880$	$192$	$3$	$0.674469705$	$1$	$11$	$2304$	$1.268106$	$46424454082884/26794860125$	$1.13955$	$5.66383$	$[0, 0, 0, -7547, 12986]$	$y^2=x^3-7547x+12986$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.1, 10.6.0.a.1, 20.24.0-20.g.1.2, $\ldots$	$[(97, 440)]$
880.g2	880c2	880.g	880c	$4$	$4$	$ 2^{4} \cdot 5 \cdot 11 $	$ 2^{8} \cdot 5^{6} \cdot 11^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.24.0.7	2Cs	$440$	$192$	$3$	$1.348939411$	$1$	$9$	$1152$	$0.921533$	$55537159171536/228765625$	$1.14096$	$5.48579$	$[0, 0, 0, -5047, -137514]$	$y^2=x^3-5047x-137514$	2.6.0.a.1, 4.24.0-4.a.1.1, 20.48.0-20.b.1.1, 40.96.0-40.g.1.1, 88.48.0.?, $\ldots$	$[(137, 1320)]$
880.g3	880c1	880.g	880c	$4$	$4$	$ 2^{4} \cdot 5 \cdot 11 $	$ 2^{4} \cdot 5^{3} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.57	2B	$880$	$192$	$3$	$2.697878822$	$1$	$3$	$576$	$0.574959$	$885956203616256/15125$	$1.05882$	$5.48535$	$[0, 0, 0, -5042, -137801]$	$y^2=x^3-5042x-137801$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.o.1.3, 10.6.0.a.1, 20.24.0-20.g.1.1, $\ldots$	$[(103, 660)]$
880.g4	880c4	880.g	880c	$4$	$4$	$ 2^{4} \cdot 5 \cdot 11 $	$ - 2^{10} \cdot 5^{12} \cdot 11^{2} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.24.0.11	2B	$880$	$192$	$3$	$2.697878822$	$1$	$7$	$2304$	$1.268106$	$-1957960715364/29541015625$	$1.10389$	$5.68338$	$[0, 0, 0, -2627, -269646]$	$y^2=x^3-2627x-269646$	2.3.0.a.1, 4.24.0-4.d.1.1, 40.48.0-40.w.1.1, 44.48.0-44.d.1.2, 80.96.0.?, $\ldots$	$[(83, 290)]$
880.h1	880i3	880.h	880i	$4$	$4$	$ 2^{4} \cdot 5 \cdot 11 $	$ 2^{12} \cdot 5^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$440$	$48$	$0$	$1$	$1$	$1$	$256$	$0.407482$	$22930509321/6875$	$1.07717$	$4.74541$	$[0, 0, 0, -947, -11214]$	$y^2=x^3-947x-11214$	2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.z.1.12, 44.24.0-44.h.1.1, 440.48.0.?	$[ ]$
880.h2	880i4	880.h	880i	$4$	$4$	$ 2^{4} \cdot 5 \cdot 11 $	$ 2^{12} \cdot 5 \cdot 11^{4} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$440$	$48$	$0$	$1$	$1$	$3$	$256$	$0.407482$	$2749884201/73205$	$0.94591$	$4.43259$	$[0, 0, 0, -467, 3794]$	$y^2=x^3-467x+3794$	2.3.0.a.1, 4.12.0-4.c.1.1, 10.6.0.a.1, 20.24.0-20.g.1.2, 88.24.0.?, $\ldots$	$[ ]$
880.h3	880i2	880.h	880i	$4$	$4$	$ 2^{4} \cdot 5 \cdot 11 $	$ 2^{12} \cdot 5^{2} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$220$	$48$	$0$	$1$	$1$	$3$	$128$	$0.060908$	$8120601/3025$	$1.05560$	$3.57345$	$[0, 0, 0, -67, -126]$	$y^2=x^3-67x-126$	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.1, 44.24.0-44.a.1.2, 220.48.0.?	$[ ]$
880.h4	880i1	880.h	880i	$4$	$4$	$ 2^{4} \cdot 5 \cdot 11 $	$ - 2^{12} \cdot 5 \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$440$	$48$	$0$	$1$	$1$	$1$	$64$	$-0.285666$	$59319/55$	$0.79207$	$2.84789$	$[0, 0, 0, 13, -14]$	$y^2=x^3+13x-14$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 20.12.0-4.c.1.1, 40.24.0-40.z.1.2, $\ldots$	$[ ]$
880.i1	880g2	880.i	880g	$2$	$5$	$ 2^{4} \cdot 5 \cdot 11 $	$ - 2^{13} \cdot 5 \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$440$	$48$	$1$	$0.635564849$	$1$	$4$	$2400$	$1.338223$	$-23178622194826561/1610510$	$1.01294$	$6.78471$	$[0, 1, 0, -95040, 11245748]$	$y^2=x^3+x^2-95040x+11245748$	5.12.0.a.2, 20.24.0-5.a.2.2, 440.48.1.?	$[(178, 8)]$
880.i2	880g1	880.i	880g	$2$	$5$	$ 2^{4} \cdot 5 \cdot 11 $	$ - 2^{17} \cdot 5^{5} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$440$	$48$	$1$	$0.127112969$	$1$	$8$	$480$	$0.533504$	$109902239/1100000$	$0.94438$	$4.36933$	$[0, 1, 0, 160, 3188]$	$y^2=x^3+x^2+160x+3188$	5.12.0.a.1, 20.24.0-5.a.1.2, 440.48.1.?	$[(26, 160)]$
880.j1	880j4	880.j	880j	$4$	$6$	$ 2^{4} \cdot 5 \cdot 11 $	$ 2^{8} \cdot 5^{2} \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$660$	$96$	$1$	$1$	$1$	$1$	$864$	$0.714450$	$154639330142416/33275$	$0.97344$	$5.63683$	$[0, -1, 0, -7100, 232652]$	$y^2=x^3-x^2-7100x+232652$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0-6.a.1.9, 20.6.0.c.1, $\ldots$	$[ ]$
880.j2	880j3	880.j	880j	$4$	$6$	$ 2^{4} \cdot 5 \cdot 11 $	$ 2^{4} \cdot 5 \cdot 11^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$660$	$96$	$1$	$1$	$1$	$1$	$432$	$0.367877$	$610462990336/8857805$	$1.02612$	$4.41157$	$[0, -1, 0, -445, 3720]$	$y^2=x^3-x^2-445x+3720$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 10.6.0.a.1, 12.24.0-6.a.1.9, $\ldots$	$[ ]$
880.j3	880j2	880.j	880j	$4$	$6$	$ 2^{4} \cdot 5 \cdot 11 $	$ 2^{8} \cdot 5^{6} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$660$	$96$	$1$	$1$	$1$	$1$	$288$	$0.165144$	$436334416/171875$	$0.87819$	$3.75212$	$[0, -1, 0, -100, 252]$	$y^2=x^3-x^2-100x+252$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0-6.a.1.3, 20.6.0.c.1, $\ldots$	$[ ]$
880.j4	880j1	880.j	880j	$4$	$6$	$ 2^{4} \cdot 5 \cdot 11 $	$ 2^{4} \cdot 5^{3} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$660$	$96$	$1$	$1$	$1$	$1$	$144$	$-0.181429$	$643956736/15125$	$0.96705$	$3.40059$	$[0, -1, 0, -45, -100]$	$y^2=x^3-x^2-45x-100$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 10.6.0.a.1, 12.24.0-6.a.1.3, $\ldots$	$[ ]$

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 (25 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 (25 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