LMFDB - Elliptic curves over $\Q$ of conductor 1984

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 (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
1984.a1	1984l2	1984.a	1984l	$2$	$2$	$ 2^{6} \cdot 31 $	$ 2^{17} \cdot 31^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$248$	$12$	$0$	$0.592896232$	$1$	$7$	$512$	$0.245914$	$1825346/961$	$0.88772$	$3.45071$	$[0, 1, 0, -129, 127]$	$y^2=x^3+x^2-129x+127$	2.3.0.a.1, 8.6.0.b.1, 124.6.0.?, 248.12.0.?	$[(-1, 16)]$
1984.a2	1984l1	1984.a	1984l	$2$	$2$	$ 2^{6} \cdot 31 $	$ - 2^{16} \cdot 31 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$248$	$12$	$0$	$1.185792464$	$1$	$5$	$256$	$-0.100659$	$48668/31$	$0.79741$	$2.88206$	$[0, 1, 0, 31, 31]$	$y^2=x^3+x^2+31x+31$	2.3.0.a.1, 8.6.0.c.1, 62.6.0.b.1, 248.12.0.?	$[(1, 8)]$
1984.b1	1984k1	1984.b	1984k	$1$	$1$	$ 2^{6} \cdot 31 $	$ - 2^{10} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$62$	$2$	$0$	$1.338685407$	$1$	$2$	$128$	$-0.456748$	$-256/31$	$0.78373$	$2.34759$	$[0, 1, 0, -1, -9]$	$y^2=x^3+x^2-x-9$	62.2.0.a.1	$[(2, 1)]$
1984.c1	1984h1	1984.c	1984h	$2$	$3$	$ 2^{6} \cdot 31 $	$ - 2^{10} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$744$	$16$	$0$	$1$	$1$	$0$	$192$	$-0.425188$	$-87808/31$	$0.69864$	$2.47478$	$[0, 1, 0, -9, -17]$	$y^2=x^3+x^2-9x-17$	3.4.0.a.1, 24.8.0-3.a.1.4, 62.2.0.a.1, 186.8.0.?, 744.16.0.?	$[]$
1984.c2	1984h2	1984.c	1984h	$2$	$3$	$ 2^{6} \cdot 31 $	$ - 2^{10} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$744$	$16$	$0$	$1$	$1$	$0$	$576$	$0.124118$	$38112512/29791$	$0.88754$	$3.21190$	$[0, 1, 0, 71, 159]$	$y^2=x^3+x^2+71x+159$	3.4.0.a.1, 24.8.0-3.a.1.3, 62.2.0.a.1, 186.8.0.?, 744.16.0.?	$[]$
1984.d1	1984i1	1984.d	1984i	$1$	$1$	$ 2^{6} \cdot 31 $	$ - 2^{10} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$62$	$2$	$0$	$0.741926569$	$1$	$2$	$192$	$-0.212415$	$-33958656/31$	$1.22690$	$3.19691$	$[0, 0, 0, -68, 216]$	$y^2=x^3-68x+216$	62.2.0.a.1	$[(5, 1)]$
1984.e1	1984a1	1984.e	1984a	$1$	$1$	$ 2^{6} \cdot 31 $	$ - 2^{10} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$62$	$2$	$0$	$3.519326017$	$1$	$2$	$192$	$-0.212415$	$-33958656/31$	$1.22690$	$3.19691$	$[0, 0, 0, -68, -216]$	$y^2=x^3-68x-216$	62.2.0.a.1	$[(29, 149)]$
1984.f1	1984b4	1984.f	1984b	$4$	$4$	$ 2^{6} \cdot 31 $	$ 2^{19} \cdot 31 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.50	2B	$248$	$48$	$0$	$8.147347663$	$1$	$3$	$1536$	$0.931643$	$3999236143617/62$	$1.07559$	$5.46483$	$[0, 0, 0, -21164, 1185072]$	$y^2=x^3-21164x+1185072$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.1, 248.48.0.?	$[(11704/9, 779660/9)]$
1984.f2	1984b3	1984.f	1984b	$4$	$4$	$ 2^{6} \cdot 31 $	$ 2^{19} \cdot 31^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.58	2B	$248$	$48$	$0$	$2.036836915$	$1$	$3$	$1536$	$0.931643$	$3196010817/1847042$	$1.17908$	$4.52554$	$[0, 0, 0, -1964, -1232]$	$y^2=x^3-1964x-1232$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.k.1.1, 248.48.0.?	$[(54, 224)]$
1984.f3	1984b2	1984.f	1984b	$4$	$4$	$ 2^{6} \cdot 31 $	$ 2^{20} \cdot 31^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.1	2Cs	$248$	$48$	$0$	$4.073673831$	$1$	$5$	$768$	$0.585070$	$979146657/3844$	$1.02504$	$4.36974$	$[0, 0, 0, -1324, 18480]$	$y^2=x^3-1324x+18480$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.2, 124.24.0.?, 248.48.0.?	$[(120, 1260)]$
1984.f4	1984b1	1984.f	1984b	$4$	$4$	$ 2^{6} \cdot 31 $	$ - 2^{22} \cdot 31 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.103	2B	$248$	$48$	$0$	$2.036836915$	$1$	$5$	$384$	$0.238496$	$-35937/496$	$0.93090$	$3.44784$	$[0, 0, 0, -44, 560]$	$y^2=x^3-44x+560$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.7, 62.6.0.b.1, 124.12.0.?, $\ldots$	$[(-8, 20)]$
1984.g1	1984j3	1984.g	1984j	$4$	$4$	$ 2^{6} \cdot 31 $	$ 2^{19} \cdot 31 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.60	2B	$248$	$48$	$0$	$16.15697718$	$1$	$1$	$1536$	$0.931643$	$3999236143617/62$	$1.07559$	$5.46483$	$[0, 0, 0, -21164, -1185072]$	$y^2=x^3-21164x-1185072$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.p.1.3, 248.48.0.?	$[(13874604/287, 4048997280/287)]$
1984.g2	1984j4	1984.g	1984j	$4$	$4$	$ 2^{6} \cdot 31 $	$ 2^{19} \cdot 31^{4} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.49	2B	$248$	$48$	$0$	$4.039244295$	$1$	$3$	$1536$	$0.931643$	$3196010817/1847042$	$1.17908$	$4.52554$	$[0, 0, 0, -1964, 1232]$	$y^2=x^3-1964x+1232$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.k.1.2, 248.48.0.?	$[(-326/3, 4256/3)]$
1984.g3	1984j2	1984.g	1984j	$4$	$4$	$ 2^{6} \cdot 31 $	$ 2^{20} \cdot 31^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.2	2Cs	$248$	$48$	$0$	$8.078488591$	$1$	$3$	$768$	$0.585070$	$979146657/3844$	$1.02504$	$4.36974$	$[0, 0, 0, -1324, -18480]$	$y^2=x^3-1324x-18480$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.1, 124.24.0.?, 248.48.0.?	$[(5420/7, 373920/7)]$
1984.g4	1984j1	1984.g	1984j	$4$	$4$	$ 2^{6} \cdot 31 $	$ - 2^{22} \cdot 31 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.101	2B	$248$	$48$	$0$	$4.039244295$	$1$	$3$	$384$	$0.238496$	$-35937/496$	$0.93090$	$3.44784$	$[0, 0, 0, -44, -560]$	$y^2=x^3-44x-560$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.5, 62.6.0.b.1, 124.12.0.?, $\ldots$	$[(108, 1120)]$
1984.h1	1984e1	1984.h	1984e	$1$	$1$	$ 2^{6} \cdot 31 $	$ - 2^{10} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$62$	$2$	$0$	$1$	$1$	$0$	$128$	$-0.453764$	$6912/31$	$0.65713$	$2.32877$	$[0, 0, 0, 4, -8]$	$y^2=x^3+4x-8$	62.2.0.a.1	$[]$
1984.i1	1984g1	1984.i	1984g	$1$	$1$	$ 2^{6} \cdot 31 $	$ - 2^{10} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$62$	$2$	$0$	$1$	$1$	$0$	$128$	$-0.453764$	$6912/31$	$0.65713$	$2.32877$	$[0, 0, 0, 4, 8]$	$y^2=x^3+4x+8$	62.2.0.a.1	$[]$
1984.j1	1984d2	1984.j	1984d	$2$	$2$	$ 2^{6} \cdot 31 $	$ 2^{17} \cdot 31^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$248$	$12$	$0$	$1.189780476$	$1$	$3$	$512$	$0.245914$	$1825346/961$	$0.88772$	$3.45071$	$[0, -1, 0, -129, -127]$	$y^2=x^3-x^2-129x-127$	2.3.0.a.1, 8.6.0.b.1, 124.6.0.?, 248.12.0.?	$[(17, 48)]$
1984.j2	1984d1	1984.j	1984d	$2$	$2$	$ 2^{6} \cdot 31 $	$ - 2^{16} \cdot 31 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$248$	$12$	$0$	$2.379560952$	$1$	$3$	$256$	$-0.100659$	$48668/31$	$0.79741$	$2.88206$	$[0, -1, 0, 31, -31]$	$y^2=x^3-x^2+31x-31$	2.3.0.a.1, 8.6.0.c.1, 62.6.0.b.1, 248.12.0.?	$[(19, 84)]$
1984.k1	1984c1	1984.k	1984c	$1$	$1$	$ 2^{6} \cdot 31 $	$ - 2^{10} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$62$	$2$	$0$	$1.191034796$	$1$	$2$	$128$	$-0.456748$	$-256/31$	$0.78373$	$2.34759$	$[0, -1, 0, -1, 9]$	$y^2=x^3-x^2-x+9$	62.2.0.a.1	$[(0, 3)]$
1984.l1	1984f1	1984.l	1984f	$2$	$3$	$ 2^{6} \cdot 31 $	$ - 2^{10} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$744$	$16$	$0$	$1$	$1$	$0$	$192$	$-0.425188$	$-87808/31$	$0.69864$	$2.47478$	$[0, -1, 0, -9, 17]$	$y^2=x^3-x^2-9x+17$	3.4.0.a.1, 24.8.0-3.a.1.2, 62.2.0.a.1, 186.8.0.?, 744.16.0.?	$[]$
1984.l2	1984f2	1984.l	1984f	$2$	$3$	$ 2^{6} \cdot 31 $	$ - 2^{10} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$744$	$16$	$0$	$1$	$1$	$0$	$576$	$0.124118$	$38112512/29791$	$0.88754$	$3.21190$	$[0, -1, 0, 71, -159]$	$y^2=x^3-x^2+71x-159$	3.4.0.a.1, 24.8.0-3.a.1.1, 62.2.0.a.1, 186.8.0.?, 744.16.0.?	$[]$

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 (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