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 (24 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	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
6534.f1	6534e1	6534.f	6534e	$1$	$1$	$ 2 \cdot 3^{3} \cdot 11^{2} $	$ 2^{11} \cdot 3^{11} \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$	$0$	$4752$	$0.747230$	$6777507/2048$	$0.96170$	$3.71206$	$[1, -1, 0, -1095, 9917]$	$y^2+xy=x^3-x^2-1095x+9917$	24.2.0.a.1	$[]$
6534.i1	6534d1	6534.i	6534d	$1$	$1$	$ 2 \cdot 3^{3} \cdot 11^{2} $	$ 2^{11} \cdot 3^{5} \cdot 11^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$	$0$	$17424$	$1.396872$	$6777507/2048$	$0.96170$	$4.59947$	$[1, -1, 0, -14724, 479056]$	$y^2+xy=x^3-x^2-14724x+479056$	24.2.0.a.1	$[]$
6534.v1	6534t1	6534.v	6534t	$1$	$1$	$ 2 \cdot 3^{3} \cdot 11^{2} $	$ 2^{11} \cdot 3^{11} \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$0.704910845$	$1$	$4$	$52272$	$1.946177$	$6777507/2048$	$0.96170$	$5.34983$	$[1, -1, 1, -132518, -12801995]$	$y^2+xy+y=x^3-x^2-132518x-12801995$	24.2.0.a.1	$[(-151, 2011)]$
6534.z1	6534s1	6534.z	6534s	$1$	$1$	$ 2 \cdot 3^{3} \cdot 11^{2} $	$ 2^{11} \cdot 3^{5} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$0.124641153$	$1$	$10$	$1584$	$0.197923$	$6777507/2048$	$0.96170$	$2.96171$	$[1, -1, 1, -122, -327]$	$y^2+xy+y=x^3-x^2-122x-327$	24.2.0.a.1	$[(-7, 15)]$
52272.z1	52272cz1	52272.z	52272cz	$1$	$1$	$ 2^{4} \cdot 3^{3} \cdot 11^{2} $	$ 2^{23} \cdot 3^{11} \cdot 11^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$	$0$	$1254528$	$2.639324$	$6777507/2048$	$0.96170$	$5.09147$	$[0, 0, 0, -2120283, 821447946]$	$y^2=x^3-2120283x+821447946$	24.2.0.a.1	$[]$
52272.ba1	52272cy1	52272.ba	52272cy	$1$	$1$	$ 2^{4} \cdot 3^{3} \cdot 11^{2} $	$ 2^{23} \cdot 3^{11} \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$	$0$	$114048$	$1.440376$	$6777507/2048$	$0.96170$	$3.76718$	$[0, 0, 0, -17523, -617166]$	$y^2=x^3-17523x-617166$	24.2.0.a.1	$[]$
52272.cd1	52272cx1	52272.cd	52272cx	$1$	$1$	$ 2^{4} \cdot 3^{3} \cdot 11^{2} $	$ 2^{23} \cdot 3^{5} \cdot 11^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$	$0$	$418176$	$2.090019$	$6777507/2048$	$0.96170$	$4.48473$	$[0, 0, 0, -235587, -30423998]$	$y^2=x^3-235587x-30423998$	24.2.0.a.1	$[]$
52272.ce1	52272cw1	52272.ce	52272cw	$1$	$1$	$ 2^{4} \cdot 3^{3} \cdot 11^{2} $	$ 2^{23} \cdot 3^{5} \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$	$0$	$38016$	$0.891070$	$6777507/2048$	$0.96170$	$3.16044$	$[0, 0, 0, -1947, 22858]$	$y^2=x^3-1947x+22858$	24.2.0.a.1	$[]$
163350.bc1	163350fq1	163350.bc	163350fq	$1$	$1$	$ 2 \cdot 3^{3} \cdot 5^{2} \cdot 11^{2} $	$ 2^{11} \cdot 3^{11} \cdot 5^{6} \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$11.49525447$	$1$	$0$	$7318080$	$2.750896$	$6777507/2048$	$0.96170$	$4.71970$	$[1, -1, 0, -3312942, -1603562284]$	$y^2+xy=x^3-x^2-3312942x-1603562284$	24.2.0.a.1	$[(-842657/39, 481933271/39)]$
163350.dj1	163350gd1	163350.dj	163350gd	$1$	$1$	$ 2 \cdot 3^{3} \cdot 5^{2} \cdot 11^{2} $	$ 2^{11} \cdot 3^{5} \cdot 5^{6} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$9.872591613$	$1$	$0$	$221760$	$1.002642$	$6777507/2048$	$0.96170$	$2.97198$	$[1, -1, 0, -3042, -43884]$	$y^2+xy=x^3-x^2-3042x-43884$	24.2.0.a.1	$[(-13337/19, 1022372/19)]$
163350.fj1	163350be1	163350.fj	163350be	$1$	$1$	$ 2 \cdot 3^{3} \cdot 5^{2} \cdot 11^{2} $	$ 2^{11} \cdot 3^{5} \cdot 5^{6} \cdot 11^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$	$0$	$2439360$	$2.201591$	$6777507/2048$	$0.96170$	$4.17056$	$[1, -1, 1, -368105, 59513897]$	$y^2+xy+y=x^3-x^2-368105x+59513897$	24.2.0.a.1	$[]$
163350.hq1	163350bs1	163350.hq	163350bs	$1$	$1$	$ 2 \cdot 3^{3} \cdot 5^{2} \cdot 11^{2} $	$ 2^{11} \cdot 3^{11} \cdot 5^{6} \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$	$0$	$665280$	$1.551949$	$6777507/2048$	$0.96170$	$3.52112$	$[1, -1, 1, -27380, 1212247]$	$y^2+xy+y=x^3-x^2-27380x+1212247$	24.2.0.a.1	$[]$
209088.cp1	209088ek1	209088.cp	209088ek	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 11^{2} $	$ 2^{29} \cdot 3^{5} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$3.799799687$	$1$	$2$	$304128$	$1.237644$	$6777507/2048$	$0.96170$	$3.14229$	$[0, 0, 0, -7788, -182864]$	$y^2=x^3-7788x-182864$	24.2.0.a.1	$[(-72, 68)]$
209088.cq1	209088cp1	209088.cq	209088cp	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 11^{2} $	$ 2^{29} \cdot 3^{5} \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$6.148088645$	$1$	$2$	$3345408$	$2.436592$	$6777507/2048$	$0.96170$	$4.31672$	$[0, 0, 0, -942348, -243391984]$	$y^2=x^3-942348x-243391984$	24.2.0.a.1	$[(-755, 6141)]$
209088.cv1	209088cq1	209088.cv	209088cq	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 11^{2} $	$ 2^{29} \cdot 3^{5} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$0.972143963$	$1$	$4$	$304128$	$1.237644$	$6777507/2048$	$0.96170$	$3.14229$	$[0, 0, 0, -7788, 182864]$	$y^2=x^3-7788x+182864$	24.2.0.a.1	$[(122, 1024)]$
209088.cw1	209088en1	209088.cw	209088en	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 11^{2} $	$ 2^{29} \cdot 3^{5} \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$3.509839909$	$1$	$0$	$3345408$	$2.436592$	$6777507/2048$	$0.96170$	$4.31672$	$[0, 0, 0, -942348, 243391984]$	$y^2=x^3-942348x+243391984$	24.2.0.a.1	$[(9438/7, 2849792/7)]$
209088.fd1	209088de1	209088.fd	209088de	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 11^{2} $	$ 2^{29} \cdot 3^{11} \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$4.278860519$	$1$	$2$	$10036224$	$2.985897$	$6777507/2048$	$0.96170$	$4.85479$	$[0, 0, 0, -8481132, 6571583568]$	$y^2=x^3-8481132x+6571583568$	24.2.0.a.1	$[(94138, 28869632)]$
209088.fe1	209088ey1	209088.fe	209088ey	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 11^{2} $	$ 2^{29} \cdot 3^{11} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$5.023205410$	$1$	$0$	$912384$	$1.786951$	$6777507/2048$	$0.96170$	$3.68036$	$[0, 0, 0, -70092, 4937328]$	$y^2=x^3-70092x+4937328$	24.2.0.a.1	$[(-2114/5, 400384/5)]$
209088.fj1	209088fb1	209088.fj	209088fb	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 11^{2} $	$ 2^{29} \cdot 3^{11} \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$52.88923498$	$1$	$0$	$10036224$	$2.985897$	$6777507/2048$	$0.96170$	$4.85479$	$[0, 0, 0, -8481132, -6571583568]$	$y^2=x^3-8481132x-6571583568$	24.2.0.a.1	$[(-135685194020428045801832/8058395567, 23560556123799873667141641763008812/8058395567)]$
209088.fk1	209088df1	209088.fk	209088df	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 11^{2} $	$ 2^{29} \cdot 3^{11} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$17.15462308$	$1$	$0$	$912384$	$1.786951$	$6777507/2048$	$0.96170$	$3.68036$	$[0, 0, 0, -70092, -4937328]$	$y^2=x^3-70092x-4937328$	24.2.0.a.1	$[(-14423723/341, 53909867519/341)]$
320166.bp1	320166bp1	320166.bp	320166bp	$1$	$1$	$ 2 \cdot 3^{3} \cdot 7^{2} \cdot 11^{2} $	$ 2^{11} \cdot 3^{5} \cdot 7^{6} \cdot 11^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$	$0$	$6272640$	$2.369827$	$6777507/2048$	$0.96170$	$4.10842$	$[1, -1, 0, -721485, -162873243]$	$y^2+xy=x^3-x^2-721485x-162873243$	24.2.0.a.1	$[]$
320166.cw1	320166cw1	320166.cw	320166cw	$1$	$1$	$ 2 \cdot 3^{3} \cdot 7^{2} \cdot 11^{2} $	$ 2^{11} \cdot 3^{11} \cdot 7^{6} \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$	$0$	$1710720$	$1.720184$	$6777507/2048$	$0.96170$	$3.49345$	$[1, -1, 0, -53664, -3294208]$	$y^2+xy=x^3-x^2-53664x-3294208$	24.2.0.a.1	$[]$
320166.fv1	320166fv1	320166.fv	320166fv	$1$	$1$	$ 2 \cdot 3^{3} \cdot 7^{2} \cdot 11^{2} $	$ 2^{11} \cdot 3^{5} \cdot 7^{6} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$0.723350879$	$1$	$4$	$570240$	$1.170877$	$6777507/2048$	$0.96170$	$2.97347$	$[1, -1, 1, -5963, 123995]$	$y^2+xy+y=x^3-x^2-5963x+123995$	24.2.0.a.1	$[(-5, 394)]$
320166.he1	320166he1	320166.he	320166he	$1$	$1$	$ 2 \cdot 3^{3} \cdot 7^{2} \cdot 11^{2} $	$ 2^{11} \cdot 3^{11} \cdot 7^{6} \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$2.003458892$	$1$	$2$	$18817920$	$2.919132$	$6777507/2048$	$0.96170$	$4.62841$	$[1, -1, 1, -6493367, 4404070927]$	$y^2+xy+y=x^3-x^2-6493367x+4404070927$	24.2.0.a.1	$[(-2329, 84170)]$

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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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