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	Manin constant

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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	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
4140.c2	4140a1	4140.c	4140a	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 $	$ 2^{4} \cdot 3^{3} \cdot 5^{8} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$2.461795860$	$1$		$3$	$1920$	$0.568615$	$69657034752/8984375$	$1.15465$	$3.72642$	$[0, 0, 0, -648, 5597]$	$y^2=x^3-648x+5597$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[(19, 12)]$
4140.g2	4140b1	4140.g	4140b	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 $	$ 2^{4} \cdot 3^{9} \cdot 5^{8} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$0.541714925$	$1$		$9$	$5760$	$1.117920$	$69657034752/8984375$	$1.15465$	$4.51788$	$[0, 0, 0, -5832, -151119]$	$y^2=x^3-5832x-151119$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[(-48, 135)]$
16560.o2	16560y1	16560.o	16560y	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 23 $	$ 2^{4} \cdot 3^{3} \cdot 5^{8} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$1$	$7680$	$0.568615$	$69657034752/8984375$	$1.15465$	$3.19466$	$[0, 0, 0, -648, -5597]$	$y^2=x^3-648x-5597$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[ ]$
16560.cb2	16560bf1	16560.cb	16560bf	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 23 $	$ 2^{4} \cdot 3^{9} \cdot 5^{8} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$1$	$23040$	$1.117920$	$69657034752/8984375$	$1.15465$	$3.87318$	$[0, 0, 0, -5832, 151119]$	$y^2=x^3-5832x+151119$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[ ]$
20700.l2	20700c1	20700.l	20700c	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 23 $	$ 2^{4} \cdot 3^{9} \cdot 5^{14} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$10.73080274$	$1$		$1$	$138240$	$1.922640$	$69657034752/8984375$	$1.15465$	$4.75791$	$[0, 0, 0, -145800, -18889875]$	$y^2=x^3-145800x-18889875$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[(-133445/29, 12189700/29)]$
20700.n2	20700a1	20700.n	20700a	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 23 $	$ 2^{4} \cdot 3^{3} \cdot 5^{14} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$1$	$46080$	$1.373333$	$69657034752/8984375$	$1.15465$	$4.09462$	$[0, 0, 0, -16200, 699625]$	$y^2=x^3-16200x+699625$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[ ]$
66240.z2	66240f1	66240.z	66240f	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 23 $	$ 2^{10} \cdot 3^{9} \cdot 5^{8} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$8.184875592$	$1$		$1$	$184320$	$1.464495$	$69657034752/8984375$	$1.15465$	$3.76414$	$[0, 0, 0, -23328, -1208952]$	$y^2=x^3-23328x-1208952$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[(5026/5, 186524/5)]$
66240.ck2	66240dq1	66240.ck	66240dq	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 23 $	$ 2^{10} \cdot 3^{9} \cdot 5^{8} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$5.886909323$	$1$		$3$	$184320$	$1.464495$	$69657034752/8984375$	$1.15465$	$3.76414$	$[0, 0, 0, -23328, 1208952]$	$y^2=x^3-23328x+1208952$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[(3714, 226152)]$
66240.dv2	66240x1	66240.dv	66240x	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 23 $	$ 2^{10} \cdot 3^{3} \cdot 5^{8} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$0.706059715$	$1$		$7$	$61440$	$0.915188$	$69657034752/8984375$	$1.15465$	$3.17035$	$[0, 0, 0, -2592, 44776]$	$y^2=x^3-2592x+44776$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[(17, 75)]$
66240.fp2	66240dy1	66240.fp	66240dy	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 23 $	$ 2^{10} \cdot 3^{3} \cdot 5^{8} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$1.494528070$	$1$		$3$	$61440$	$0.915188$	$69657034752/8984375$	$1.15465$	$3.17035$	$[0, 0, 0, -2592, -44776]$	$y^2=x^3-2592x-44776$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[(-22, 40)]$
82800.bl2	82800cr1	82800.bl	82800cr	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 23 $	$ 2^{4} \cdot 3^{3} \cdot 5^{14} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$6.505241382$	$1$		$1$	$184320$	$1.373333$	$69657034752/8984375$	$1.15465$	$3.59336$	$[0, 0, 0, -16200, -699625]$	$y^2=x^3-16200x-699625$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[(-3335/8, 28275/8)]$
82800.bz2	82800ck1	82800.bz	82800ck	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 23 $	$ 2^{4} \cdot 3^{9} \cdot 5^{14} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$1$	$552960$	$1.922640$	$69657034752/8984375$	$1.15465$	$4.17545$	$[0, 0, 0, -145800, 18889875]$	$y^2=x^3-145800x+18889875$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[ ]$
95220.n2	95220a1	95220.n	95220a	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 23^{2} $	$ 2^{4} \cdot 3^{9} \cdot 5^{8} \cdot 23^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$6.883434135$	$1$		$3$	$3041280$	$2.685669$	$69657034752/8984375$	$1.15465$	$4.92325$	$[0, 0, 0, -3085128, 1838664873]$	$y^2=x^3-3085128x+1838664873$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[(7746, 665361)]$
95220.w2	95220d1	95220.w	95220d	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 23^{2} $	$ 2^{4} \cdot 3^{3} \cdot 5^{8} \cdot 23^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$1$	$1013760$	$2.136360$	$69657034752/8984375$	$1.15465$	$4.34826$	$[0, 0, 0, -342792, -68098699]$	$y^2=x^3-342792x-68098699$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[ ]$
202860.d2	202860cp1	202860.d	202860cp	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 $	$ 2^{4} \cdot 3^{9} \cdot 5^{8} \cdot 7^{6} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$2.596363692$	$1$		$5$	$2073600$	$2.090878$	$69657034752/8984375$	$1.15465$	$4.03448$	$[0, 0, 0, -285768, 51833817]$	$y^2=x^3-285768x+51833817$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[(16, 6875)]$
202860.cn2	202860cj1	202860.cn	202860cj	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 $	$ 2^{4} \cdot 3^{3} \cdot 5^{8} \cdot 7^{6} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$3.506994738$	$1$		$3$	$691200$	$1.541571$	$69657034752/8984375$	$1.15465$	$3.49507$	$[0, 0, 0, -31752, -1919771]$	$y^2=x^3-31752x-1919771$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[(-117, 440)]$
331200.dw2	331200dw1	331200.dw	331200dw	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 23 $	$ 2^{10} \cdot 3^{9} \cdot 5^{14} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$1$	$4423680$	$2.269215$	$69657034752/8984375$	$1.15465$	$4.04725$	$[0, 0, 0, -583200, 151119000]$	$y^2=x^3-583200x+151119000$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[ ]$
331200.fh2	331200fh1	331200.fh	331200fh	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 23 $	$ 2^{10} \cdot 3^{3} \cdot 5^{14} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$6.816251467$	$1$		$1$	$1474560$	$1.719908$	$69657034752/8984375$	$1.15465$	$3.52865$	$[0, 0, 0, -64800, -5597000]$	$y^2=x^3-64800x-5597000$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[(-6270/7, 265600/7)]$
331200.ls2	331200ls1	331200.ls	331200ls	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 23 $	$ 2^{10} \cdot 3^{3} \cdot 5^{14} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$4.643631358$	$1$		$3$	$1474560$	$1.719908$	$69657034752/8984375$	$1.15465$	$3.52865$	$[0, 0, 0, -64800, 5597000]$	$y^2=x^3-64800x+5597000$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[(194, 572)]$
331200.nd2	331200nd1	331200.nd	331200nd	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 23 $	$ 2^{10} \cdot 3^{9} \cdot 5^{14} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$4$	$2$	$1$	$4423680$	$2.269215$	$69657034752/8984375$	$1.15465$	$4.04725$	$[0, 0, 0, -583200, -151119000]$	$y^2=x^3-583200x-151119000$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[ ]$
380880.r2	380880r1	380880.r	380880r	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 23^{2} $	$ 2^{4} \cdot 3^{9} \cdot 5^{8} \cdot 23^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$5.542309267$	$1$		$1$	$12165120$	$2.685669$	$69657034752/8984375$	$1.15465$	$4.39213$	$[0, 0, 0, -3085128, -1838664873]$	$y^2=x^3-3085128x-1838664873$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[(-60927/7, 2970864/7)]$
380880.en2	380880en1	380880.en	380880en	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 23^{2} $	$ 2^{4} \cdot 3^{3} \cdot 5^{8} \cdot 23^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$1$	$4055040$	$2.136360$	$69657034752/8984375$	$1.15465$	$3.87917$	$[0, 0, 0, -342792, 68098699]$	$y^2=x^3-342792x+68098699$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[ ]$
476100.ba2	476100ba1	476100.ba	476100ba	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 23^{2} $	$ 2^{4} \cdot 3^{3} \cdot 5^{14} \cdot 23^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$5.110812666$	$1$		$1$	$24330240$	$2.941082$	$69657034752/8984375$	$1.15465$	$4.55160$	$[0, 0, 0, -8569800, -8512337375]$	$y^2=x^3-8569800x-8512337375$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[(-12305/3, 687700/3)]$
476100.bh2	476100bh1	476100.bh	476100bh	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 23^{2} $	$ 2^{4} \cdot 3^{9} \cdot 5^{14} \cdot 23^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$276$	$12$	$0$	$17.00851183$	$1$		$1$	$72990720$	$3.490387$	$69657034752/8984375$	$1.15465$	$5.05581$	$[0, 0, 0, -77128200, 229833109125]$	$y^2=x^3-77128200x+229833109125$	2.3.0.a.1, 12.6.0.b.1, 92.6.0.?, 138.6.0.?, 276.12.0.?	$[(2332765915/937, 171895590033400/937)]$

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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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