LMFDB - Elliptic curve search results

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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

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Results (22 matches)

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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.l2	9240h3	9240.l	9240h	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{2} \cdot 5^{4} \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$3080$	$48$	$0$	$0.731210649$	$1$	$7$	$12288$	$0.886736$	$1729010797924/148561875$	$0.89333$	$3.84502$	$[0, -1, 0, -2520, -44100]$	$y^2=x^3-x^2-2520x-44100$	2.3.0.a.1, 4.12.0-4.c.1.2, 44.24.0-44.h.1.1, 280.24.0.?, 3080.48.0.?	$[(-30, 60)]$
18480.db2	18480bg4	18480.db	18480bg	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{2} \cdot 5^{4} \cdot 7^{4} \cdot 11 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$3080$	$48$	$0$	$1$	$1$	$3$	$24576$	$0.886736$	$1729010797924/148561875$	$0.89333$	$3.57374$	$[0, 1, 0, -2520, 44100]$	$y^2=x^3+x^2-2520x+44100$	2.3.0.a.1, 4.12.0-4.c.1.1, 44.24.0-44.h.1.2, 280.24.0.?, 3080.48.0.?	$[]$
27720.g2	27720bc3	27720.g	27720bc	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{8} \cdot 5^{4} \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$2.255056523$	$1$	$5$	$98304$	$1.436041$	$1729010797924/148561875$	$0.89333$	$4.07645$	$[0, 0, 0, -22683, 1213382]$	$y^2=x^3-22683x+1213382$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 44.12.0.h.1, 132.24.0.?, $\ldots$	$[(131, 700)]$
46200.da2	46200cz3	46200.da	46200cz	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{2} \cdot 5^{10} \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3080$	$48$	$0$	$1.573753846$	$1$	$7$	$294912$	$1.691454$	$1729010797924/148561875$	$0.89333$	$4.16793$	$[0, 1, 0, -63008, -5638512]$	$y^2=x^3+x^2-63008x-5638512$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 44.12.0.h.1, 56.12.0-4.c.1.5, $\ldots$	$[(-128, 588)]$
55440.cm2	55440z3	55440.cm	55440z	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{8} \cdot 5^{4} \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$	$1$	$196608$	$1.436041$	$1729010797924/148561875$	$0.89333$	$3.81777$	$[0, 0, 0, -22683, -1213382]$	$y^2=x^3-22683x-1213382$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 44.12.0.h.1, 132.24.0.?, $\ldots$	$[]$
64680.ch2	64680ba3	64680.ch	64680ba	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{10} \cdot 3^{2} \cdot 5^{4} \cdot 7^{10} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3080$	$48$	$0$	$1$	$1$	$1$	$589824$	$1.859690$	$1729010797924/148561875$	$0.89333$	$4.22358$	$[0, 1, 0, -123496, 15373280]$	$y^2=x^3+x^2-123496x+15373280$	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.1, 40.12.0-4.c.1.5, 44.12.0.h.1, $\ldots$	$[]$
73920.bo2	73920fc3	73920.bo	73920fc	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{2} \cdot 5^{4} \cdot 7^{4} \cdot 11 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$3080$	$48$	$0$	$0.766392584$	$1$	$25$	$196608$	$1.233309$	$1729010797924/148561875$	$0.89333$	$3.50280$	$[0, -1, 0, -10081, 362881]$	$y^2=x^3-x^2-10081x+362881$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 44.12.0.h.1, 88.24.0.?, $\ldots$	$[(85, 336), (21, 400)]$
73920.eh2	73920cf3	73920.eh	73920cf	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{2} \cdot 5^{4} \cdot 7^{4} \cdot 11 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$3080$	$48$	$0$	$5.911711787$	$1$	$9$	$196608$	$1.233309$	$1729010797924/148561875$	$0.89333$	$3.50280$	$[0, 1, 0, -10081, -362881]$	$y^2=x^3+x^2-10081x-362881$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 44.12.0.h.1, 88.24.0.?, $\ldots$	$[(-46, 75), (-55, 168)]$
92400.e2	92400g3	92400.e	92400g	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{2} \cdot 5^{10} \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3080$	$48$	$0$	$1.298199505$	$1$	$7$	$589824$	$1.691454$	$1729010797924/148561875$	$0.89333$	$3.91526$	$[0, -1, 0, -63008, 5638512]$	$y^2=x^3-x^2-63008x+5638512$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 44.12.0.h.1, 56.12.0-4.c.1.5, $\ldots$	$[(422, 7350)]$
101640.z2	101640ch3	101640.z	101640ch	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} $	$ 2^{10} \cdot 3^{2} \cdot 5^{4} \cdot 7^{4} \cdot 11^{7} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$3080$	$48$	$0$	$1.292255155$	$1$	$11$	$1474560$	$2.085682$	$1729010797924/148561875$	$0.89333$	$4.29322$	$[0, -1, 0, -304960, 59916892]$	$y^2=x^3-x^2-304960x+59916892$	2.3.0.a.1, 4.12.0-4.c.1.1, 44.24.0-44.h.1.2, 280.24.0.?, 3080.48.0.?	$[(169, 3630)]$
129360.d2	129360v3	129360.d	129360v	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{10} \cdot 3^{2} \cdot 5^{4} \cdot 7^{10} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3080$	$48$	$0$	$1$	$1$	$1$	$1179648$	$1.859690$	$1729010797924/148561875$	$0.89333$	$3.97486$	$[0, -1, 0, -123496, -15373280]$	$y^2=x^3-x^2-123496x-15373280$	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 40.12.0-4.c.1.5, 44.12.0.h.1, $\ldots$	$[]$
138600.cr2	138600du3	138600.cr	138600du	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{8} \cdot 5^{10} \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1.170201624$	$1$	$7$	$2359296$	$2.240761$	$1729010797924/148561875$	$0.89333$	$4.33794$	$[0, 0, 0, -567075, 151672750]$	$y^2=x^3-567075x+151672750$	2.3.0.a.1, 4.6.0.c.1, 44.12.0.h.1, 60.12.0-4.c.1.1, 168.12.0.?, $\ldots$	$[(215, 6300)]$
194040.cr2	194040m4	194040.cr	194040m	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{10} \cdot 3^{8} \cdot 5^{4} \cdot 7^{10} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$2.790522084$	$1$	$5$	$4718592$	$2.408997$	$1729010797924/148561875$	$0.89333$	$4.38387$	$[0, 0, 0, -1111467, -416190026]$	$y^2=x^3-1111467x-416190026$	2.3.0.a.1, 4.6.0.c.1, 44.12.0.h.1, 84.12.0.?, 120.12.0.?, $\ldots$	$[(-517, 4500)]$
203280.fm2	203280fa4	203280.fm	203280fa	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} $	$ 2^{10} \cdot 3^{2} \cdot 5^{4} \cdot 7^{4} \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$3080$	$48$	$0$	$1$	$1$	$1$	$2949120$	$2.085682$	$1729010797924/148561875$	$0.89333$	$4.04975$	$[0, 1, 0, -304960, -59916892]$	$y^2=x^3+x^2-304960x-59916892$	2.3.0.a.1, 4.12.0-4.c.1.2, 44.24.0-44.h.1.1, 280.24.0.?, 3080.48.0.?	$[]$
221760.ii2	221760je3	221760.ii	221760je	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{8} \cdot 5^{4} \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$	$1$	$1572864$	$1.782616$	$1729010797924/148561875$	$0.89333$	$3.72567$	$[0, 0, 0, -90732, 9707056]$	$y^2=x^3-90732x+9707056$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 44.12.0.h.1, 264.24.0.?, $\ldots$	$[]$
221760.ko2	221760t4	221760.ko	221760t	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{8} \cdot 5^{4} \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$0.880391545$	$1$	$9$	$1572864$	$1.782616$	$1729010797924/148561875$	$0.89333$	$3.72567$	$[0, 0, 0, -90732, -9707056]$	$y^2=x^3-90732x-9707056$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 44.12.0.h.1, 264.24.0.?, $\ldots$	$[(418, 5040)]$
277200.dr2	277200dr4	277200.dr	277200dr	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{8} \cdot 5^{10} \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$4.241592287$	$1$	$3$	$4718592$	$2.240761$	$1729010797924/148561875$	$0.89333$	$4.09801$	$[0, 0, 0, -567075, -151672750]$	$y^2=x^3-567075x-151672750$	2.3.0.a.1, 4.6.0.c.1, 44.12.0.h.1, 60.12.0-4.c.1.2, 168.12.0.?, $\ldots$	$[(-334, 686)]$
304920.bi2	304920bi4	304920.bi	304920bi	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} $	$ 2^{10} \cdot 3^{8} \cdot 5^{4} \cdot 7^{4} \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$	$1$	$11796480$	$2.634991$	$1729010797924/148561875$	$0.89333$	$4.44171$	$[0, 0, 0, -2744643, -1615011442]$	$y^2=x^3-2744643x-1615011442$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 44.12.0.h.1, 132.24.0.?, $\ldots$	$[]$
323400.er2	323400er3	323400.er	323400er	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ 2^{10} \cdot 3^{2} \cdot 5^{10} \cdot 7^{10} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$3080$	$48$	$0$	$1$	$1$	$1$	$14155776$	$2.664410$	$1729010797924/148561875$	$0.89333$	$4.44894$	$[0, -1, 0, -3087408, 1927834812]$	$y^2=x^3-x^2-3087408x+1927834812$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 44.12.0.h.1, 88.24.0.?, $\ldots$	$[]$
369600.jf2	369600jf4	369600.jf	369600jf	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{2} \cdot 5^{10} \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3080$	$48$	$0$	$1$	$1$	$1$	$4718592$	$2.038029$	$1729010797924/148561875$	$0.89333$	$3.81629$	$[0, -1, 0, -252033, -44856063]$	$y^2=x^3-x^2-252033x-44856063$	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.1, 44.12.0.h.1, 56.12.0-4.c.1.4, $\ldots$	$[]$
369600.qv2	369600qv3	369600.qv	369600qv	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{2} \cdot 5^{10} \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3080$	$48$	$0$	$1$	$1$	$1$	$4718592$	$2.038029$	$1729010797924/148561875$	$0.89333$	$3.81629$	$[0, 1, 0, -252033, 44856063]$	$y^2=x^3+x^2-252033x+44856063$	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.2, 44.12.0.h.1, 56.12.0-4.c.1.4, $\ldots$	$[]$
388080.lu2	388080lu3	388080.lu	388080lu	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{10} \cdot 3^{8} \cdot 5^{4} \cdot 7^{10} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1.628381464$	$1$	$7$	$9437184$	$2.408997$	$1729010797924/148561875$	$0.89333$	$4.14774$	$[0, 0, 0, -1111467, 416190026]$	$y^2=x^3-1111467x+416190026$	2.3.0.a.1, 4.6.0.c.1, 44.12.0.h.1, 84.12.0.?, 120.12.0.?, $\ldots$	$[(427, 4410)]$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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