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 (26 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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
2760.a2	2760d2	2760.a	2760d	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2760$	$48$	$0$	$1$	$1$		$3$	$768$	$0.247656$	$273671716/119025$	$0.86426$	$3.32689$	$[0, -1, 0, -136, -260]$	$y^2=x^3-x^2-136x-260$	2.6.0.a.1, 8.12.0-2.a.1.1, 60.12.0-2.a.1.1, 92.12.0.?, 120.24.0.?, $\ldots$	$[]$
5520.v2	5520g2	5520.v	5520g	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2760$	$48$	$0$	$1.289072913$	$1$		$9$	$1536$	$0.247656$	$273671716/119025$	$0.86426$	$3.05925$	$[0, 1, 0, -136, 260]$	$y^2=x^3+x^2-136x+260$	2.6.0.a.1, 8.12.0-2.a.1.1, 60.12.0-2.a.1.1, 92.12.0.?, 120.24.0.?, $\ldots$	$[(-8, 30)]$
8280.p2	8280l2	8280.p	8280l	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 $	$ 2^{10} \cdot 3^{8} \cdot 5^{2} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2760$	$48$	$0$	$1$	$1$		$3$	$6144$	$0.796963$	$273671716/119025$	$0.86426$	$3.65241$	$[0, 0, 0, -1227, 8246]$	$y^2=x^3-1227x+8246$	2.6.0.a.1, 20.12.0-2.a.1.1, 24.12.0-2.a.1.1, 120.24.0.?, 184.12.0.?, $\ldots$	$[]$
13800.w2	13800m2	13800.w	13800m	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 23 $	$ 2^{10} \cdot 3^{2} \cdot 5^{8} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2760$	$48$	$0$	$4.622918229$	$1$		$5$	$18432$	$1.052376$	$273671716/119025$	$0.86426$	$3.77821$	$[0, 1, 0, -3408, -39312]$	$y^2=x^3+x^2-3408x-39312$	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0-2.a.1.1, 120.24.0.?, 184.12.0.?, $\ldots$	$[(3188, 180000)]$
16560.bs2	16560r2	16560.bs	16560r	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 23 $	$ 2^{10} \cdot 3^{8} \cdot 5^{2} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2760$	$48$	$0$	$1.730359923$	$1$		$9$	$12288$	$0.796963$	$273671716/119025$	$0.86426$	$3.39181$	$[0, 0, 0, -1227, -8246]$	$y^2=x^3-1227x-8246$	2.6.0.a.1, 20.12.0-2.a.1.1, 24.12.0-2.a.1.1, 120.24.0.?, 184.12.0.?, $\ldots$	$[(-22, 90)]$
22080.bg2	22080ch2	22080.bg	22080ch	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{16} \cdot 3^{2} \cdot 5^{2} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2760$	$48$	$0$	$1$	$1$		$3$	$12288$	$0.594230$	$273671716/119025$	$0.86426$	$3.05104$	$[0, -1, 0, -545, 2625]$	$y^2=x^3-x^2-545x+2625$	2.6.0.a.1, 4.12.0-2.a.1.1, 120.24.0.?, 184.24.0.?, 1380.24.0.?, $\ldots$	$[]$
22080.co2	22080bj2	22080.co	22080bj	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{16} \cdot 3^{2} \cdot 5^{2} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2760$	$48$	$0$	$3.175778822$	$1$		$5$	$12288$	$0.594230$	$273671716/119025$	$0.86426$	$3.05104$	$[0, 1, 0, -545, -2625]$	$y^2=x^3+x^2-545x-2625$	2.6.0.a.1, 4.12.0-2.a.1.1, 120.24.0.?, 184.24.0.?, 1380.24.0.?, $\ldots$	$[(123, 1344)]$
27600.s2	27600b2	27600.s	27600b	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 23 $	$ 2^{10} \cdot 3^{2} \cdot 5^{8} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2760$	$48$	$0$	$1.254963758$	$1$		$13$	$36864$	$1.052376$	$273671716/119025$	$0.86426$	$3.52211$	$[0, -1, 0, -3408, 39312]$	$y^2=x^3-x^2-3408x+39312$	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0-2.a.1.1, 120.24.0.?, 184.12.0.?, $\ldots$	$[(6, 138)]$
41400.ba2	41400bm2	41400.ba	41400bm	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 23 $	$ 2^{10} \cdot 3^{8} \cdot 5^{8} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2760$	$48$	$0$	$3.029432344$	$1$		$7$	$147456$	$1.601681$	$273671716/119025$	$0.86426$	$4.00781$	$[0, 0, 0, -30675, 1030750]$	$y^2=x^3-30675x+1030750$	2.6.0.a.1, 4.12.0-2.a.1.1, 120.24.0.?, 184.24.0.?, 1380.24.0.?, $\ldots$	$[(-90, 1750)]$
63480.j2	63480l2	63480.j	63480l	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23^{2} $	$ 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 23^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2760$	$48$	$0$	$1$	$1$		$3$	$405504$	$1.815403$	$273671716/119025$	$0.86426$	$4.08482$	$[0, -1, 0, -72120, 3739932]$	$y^2=x^3-x^2-72120x+3739932$	2.6.0.a.1, 4.12.0-2.a.1.1, 120.24.0.?, 184.24.0.?, 1380.24.0.?, $\ldots$	$[]$
66240.bh2	66240ej2	66240.bh	66240ej	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 23 $	$ 2^{16} \cdot 3^{8} \cdot 5^{2} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2760$	$48$	$0$	$1.935044794$	$1$		$11$	$98304$	$1.143536$	$273671716/119025$	$0.86426$	$3.34288$	$[0, 0, 0, -4908, -65968]$	$y^2=x^3-4908x-65968$	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0-2.a.1.1, 120.24.0.?, 184.12.0.?, $\ldots$	$[(82, 288)]$
66240.bx2	66240bt2	66240.bx	66240bt	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 23 $	$ 2^{16} \cdot 3^{8} \cdot 5^{2} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2760$	$48$	$0$	$2.133783761$	$1$		$9$	$98304$	$1.143536$	$273671716/119025$	$0.86426$	$3.34288$	$[0, 0, 0, -4908, 65968]$	$y^2=x^3-4908x+65968$	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0-2.a.1.1, 120.24.0.?, 184.12.0.?, $\ldots$	$[(68, 216)]$
82800.dk2	82800bg2	82800.dk	82800bg	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 23 $	$ 2^{10} \cdot 3^{8} \cdot 5^{8} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2760$	$48$	$0$	$2.493398290$	$1$		$9$	$294912$	$1.601681$	$273671716/119025$	$0.86426$	$3.76250$	$[0, 0, 0, -30675, -1030750]$	$y^2=x^3-30675x-1030750$	2.6.0.a.1, 4.12.0-2.a.1.1, 120.24.0.?, 184.24.0.?, 1380.24.0.?, $\ldots$	$[(-55, 700)]$
110400.ch2	110400z2	110400.ch	110400z	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 23 $	$ 2^{16} \cdot 3^{2} \cdot 5^{8} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2760$	$48$	$0$	$1$	$1$		$3$	$294912$	$1.398949$	$273671716/119025$	$0.86426$	$3.45977$	$[0, -1, 0, -13633, -300863]$	$y^2=x^3-x^2-13633x-300863$	2.6.0.a.1, 20.12.0-2.a.1.1, 24.12.0-2.a.1.1, 120.24.0.?, 184.12.0.?, $\ldots$	$[]$
110400.ho2	110400hq2	110400.ho	110400hq	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 23 $	$ 2^{16} \cdot 3^{2} \cdot 5^{8} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2760$	$48$	$0$	$4.550591300$	$1$		$5$	$294912$	$1.398949$	$273671716/119025$	$0.86426$	$3.45977$	$[0, 1, 0, -13633, 300863]$	$y^2=x^3+x^2-13633x+300863$	2.6.0.a.1, 20.12.0-2.a.1.1, 24.12.0-2.a.1.1, 120.24.0.?, 184.12.0.?, $\ldots$	$[(887, 26208)]$
126960.cx2	126960r2	126960.cx	126960r	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 23^{2} $	$ 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 23^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2760$	$48$	$0$	$1$	$4$	$2$	$3$	$811008$	$1.815403$	$273671716/119025$	$0.86426$	$3.84388$	$[0, 1, 0, -72120, -3739932]$	$y^2=x^3+x^2-72120x-3739932$	2.6.0.a.1, 4.12.0-2.a.1.1, 120.24.0.?, 184.24.0.?, 1380.24.0.?, $\ldots$	$[]$
135240.dp2	135240h2	135240.dp	135240h	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 $	$ 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 7^{6} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$19320$	$48$	$0$	$4.059909055$	$1$		$5$	$294912$	$1.220612$	$273671716/119025$	$0.86426$	$3.21921$	$[0, 1, 0, -6680, 102528]$	$y^2=x^3+x^2-6680x+102528$	2.6.0.a.1, 56.12.0-2.a.1.1, 120.12.0.?, 184.12.0.?, 420.12.0.?, $\ldots$	$[(3016, 165600)]$
190440.n2	190440bk2	190440.n	190440bk	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 23^{2} $	$ 2^{10} \cdot 3^{8} \cdot 5^{2} \cdot 23^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2760$	$48$	$0$	$12.05531002$	$1$		$3$	$3244032$	$2.364708$	$273671716/119025$	$0.86426$	$4.25789$	$[0, 0, 0, -649083, -100329082]$	$y^2=x^3-649083x-100329082$	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0-2.a.1.2, 120.24.0.?, 184.12.0.?, $\ldots$	$[(-1354694/47, 850381740/47)]$
270480.cv2	270480cv2	270480.cv	270480cv	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 $	$ 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 7^{6} \cdot 23^{2} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$19320$	$48$	$0$	$2.856769080$	$1$		$27$	$589824$	$1.220612$	$273671716/119025$	$0.86426$	$3.04082$	$[0, -1, 0, -6680, -102528]$	$y^2=x^3-x^2-6680x-102528$	2.6.0.a.1, 56.12.0-2.a.1.1, 120.12.0.?, 184.12.0.?, 420.12.0.?, $\ldots$	$[(124, 980), (-23, 196)]$
317400.cb2	317400cb2	317400.cb	317400cb	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 23^{2} $	$ 2^{10} \cdot 3^{2} \cdot 5^{8} \cdot 23^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2760$	$48$	$0$	$13.40993447$	$1$		$3$	$9732096$	$2.620121$	$273671716/119025$	$0.86426$	$4.32814$	$[0, 1, 0, -1803008, 463885488]$	$y^2=x^3+x^2-1803008x+463885488$	2.6.0.a.1, 20.12.0-2.a.1.1, 24.12.0-2.a.1.2, 120.24.0.?, 184.12.0.?, $\ldots$	$[(-3592433/63, 9204749000/63)]$
331200.hw2	331200hw2	331200.hw	331200hw	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 23 $	$ 2^{16} \cdot 3^{8} \cdot 5^{8} \cdot 23^{2} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2760$	$48$	$0$	$7.372715099$	$1$		$17$	$2359296$	$1.948256$	$273671716/119025$	$0.86426$	$3.67933$	$[0, 0, 0, -122700, -8246000]$	$y^2=x^3-122700x-8246000$	2.6.0.a.1, 8.12.0-2.a.1.1, 60.12.0-2.a.1.1, 92.12.0.?, 120.24.0.?, $\ldots$	$[(-160, 2700), (416, 3564)]$
331200.jk2	331200jk2	331200.jk	331200jk	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 23 $	$ 2^{16} \cdot 3^{8} \cdot 5^{8} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2760$	$48$	$0$	$1$	$1$		$3$	$2359296$	$1.948256$	$273671716/119025$	$0.86426$	$3.67933$	$[0, 0, 0, -122700, 8246000]$	$y^2=x^3-122700x+8246000$	2.6.0.a.1, 8.12.0-2.a.1.1, 60.12.0-2.a.1.1, 92.12.0.?, 120.24.0.?, $\ldots$	$[]$
333960.p2	333960p2	333960.p	333960p	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 23 $	$ 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 11^{6} \cdot 23^{2} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$30360$	$48$	$0$	$6.014158269$	$1$		$17$	$983040$	$1.446604$	$273671716/119025$	$0.86426$	$3.20363$	$[0, -1, 0, -16496, 411996]$	$y^2=x^3-x^2-16496x+411996$	2.6.0.a.1, 88.12.0.?, 120.12.0.?, 184.12.0.?, 660.12.0.?, $\ldots$	$[(-7, 726), (-14, 800)]$
380880.bl2	380880bl2	380880.bl	380880bl	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 23^{2} $	$ 2^{10} \cdot 3^{8} \cdot 5^{2} \cdot 23^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2760$	$48$	$0$	$4.665695395$	$1$		$5$	$6488064$	$2.364708$	$273671716/119025$	$0.86426$	$4.02822$	$[0, 0, 0, -649083, 100329082]$	$y^2=x^3-649083x+100329082$	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0-2.a.1.2, 120.24.0.?, 184.12.0.?, $\ldots$	$[(1313, 38880)]$
405720.m2	405720m2	405720.m	405720m	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 $	$ 2^{10} \cdot 3^{8} \cdot 5^{2} \cdot 7^{6} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$19320$	$48$	$0$	$1$	$1$		$3$	$2359296$	$1.769918$	$273671716/119025$	$0.86426$	$3.45579$	$[0, 0, 0, -60123, -2828378]$	$y^2=x^3-60123x-2828378$	2.6.0.a.1, 120.12.0.?, 140.12.0.?, 168.12.0.?, 184.12.0.?, $\ldots$	$[]$
466440.u2	466440u2	466440.u	466440u	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 13^{2} \cdot 23 $	$ 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 13^{6} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$35880$	$48$	$0$	$1$	$1$		$3$	$1769472$	$1.530130$	$273671716/119025$	$0.86426$	$3.19842$	$[0, -1, 0, -23040, -663300]$	$y^2=x^3-x^2-23040x-663300$	2.6.0.a.1, 104.12.0.?, 120.12.0.?, 184.12.0.?, 780.12.0.?, $\ldots$	$[]$

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Elliptic curves over $\Q$
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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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