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
11424.j3	11424c1	11424.j	11424c	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$	$3$	$1792$	$0.054141$	$964430272/127449$	$0.84666$	$2.65918$	$[0, -1, 0, -82, 280]$	$y^2=x^3-x^2-82x+280$	2.6.0.a.1, 12.12.0-2.a.1.1, 56.12.0-2.a.1.1, 68.12.0-2.a.1.1, 168.24.0.?, $\ldots$	$[]$
11424.s3	11424r1	11424.s	11424r	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$3.727184453$	$1$	$5$	$1792$	$0.054141$	$964430272/127449$	$0.84666$	$2.65918$	$[0, 1, 0, -82, -280]$	$y^2=x^3+x^2-82x-280$	2.6.0.a.1, 12.12.0-2.a.1.1, 56.12.0-2.a.1.1, 68.12.0-2.a.1.1, 168.24.0.?, $\ldots$	$[(185, 2520)]$
22848.h2	22848b2	22848.h	22848b	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{12} \cdot 3^{2} \cdot 7^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$1.588521165$	$1$	$9$	$7168$	$0.400715$	$964430272/127449$	$0.84666$	$2.88990$	$[0, -1, 0, -329, -1911]$	$y^2=x^3-x^2-329x-1911$	2.6.0.a.1, 24.12.0-2.a.1.1, 28.12.0-2.a.1.1, 136.12.0.?, 168.24.0.?, $\ldots$	$[(-11, 16)]$
22848.bv2	22848bh2	22848.bv	22848bh	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{12} \cdot 3^{2} \cdot 7^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$1.770818073$	$1$	$9$	$7168$	$0.400715$	$964430272/127449$	$0.84666$	$2.88990$	$[0, 1, 0, -329, 1911]$	$y^2=x^3+x^2-329x+1911$	2.6.0.a.1, 24.12.0-2.a.1.1, 28.12.0-2.a.1.1, 136.12.0.?, 168.24.0.?, $\ldots$	$[(15, 24)]$
34272.h3	34272n1	34272.h	34272n	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{8} \cdot 7^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2856$	$48$	$0$	$1.479917801$	$1$	$9$	$14336$	$0.603448$	$964430272/127449$	$0.84666$	$3.01066$	$[0, 0, 0, -741, 6820]$	$y^2=x^3-741x+6820$	2.6.0.a.1, 4.12.0-2.a.1.1, 168.24.0.?, 204.24.0.?, 952.24.0.?, $\ldots$	$[(3, 68)]$
34272.k3	34272bm1	34272.k	34272bm	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{8} \cdot 7^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2856$	$48$	$0$	$2.707834508$	$1$	$7$	$14336$	$0.603448$	$964430272/127449$	$0.84666$	$3.01066$	$[0, 0, 0, -741, -6820]$	$y^2=x^3-741x-6820$	2.6.0.a.1, 4.12.0-2.a.1.1, 168.24.0.?, 204.24.0.?, 952.24.0.?, $\ldots$	$[(-19, 20)]$
68544.dq2	68544bl2	68544.dq	68544bl	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 17 $	$ 2^{12} \cdot 3^{8} \cdot 7^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2856$	$48$	$0$	$2.182798809$	$1$	$9$	$57344$	$0.950021$	$964430272/127449$	$0.84666$	$3.19674$	$[0, 0, 0, -2964, 54560]$	$y^2=x^3-2964x+54560$	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 204.12.0.?, $\ldots$	$[(13, 135)]$
68544.eh2	68544cl2	68544.eh	68544cl	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 17 $	$ 2^{12} \cdot 3^{8} \cdot 7^{2} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$	$3$	$57344$	$0.950021$	$964430272/127449$	$0.84666$	$3.19674$	$[0, 0, 0, -2964, -54560]$	$y^2=x^3-2964x-54560$	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 204.12.0.?, $\ldots$	$[]$
79968.i3	79968bw1	79968.i	79968bw	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 3^{2} \cdot 7^{8} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$	$3$	$86016$	$1.027096$	$964430272/127449$	$0.84666$	$3.23502$	$[0, -1, 0, -4034, 87984]$	$y^2=x^3-x^2-4034x+87984$	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 204.12.0.?, $\ldots$	$[]$
79968.bu3	79968bd1	79968.bu	79968bd	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 3^{2} \cdot 7^{8} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$	$3$	$86016$	$1.027096$	$964430272/127449$	$0.84666$	$3.23502$	$[0, 1, 0, -4034, -87984]$	$y^2=x^3+x^2-4034x-87984$	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 204.12.0.?, $\ldots$	$[]$
159936.dz2	159936jz2	159936.dz	159936jz	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{12} \cdot 3^{2} \cdot 7^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2856$	$48$	$0$	$4.353864672$	$1$	$7$	$344064$	$1.373671$	$964430272/127449$	$0.84666$	$3.39497$	$[0, -1, 0, -16137, -687735]$	$y^2=x^3-x^2-16137x-687735$	2.6.0.a.1, 4.12.0-2.a.1.1, 168.24.0.?, 204.24.0.?, 952.24.0.?, $\ldots$	$[(149, 440)]$
159936.jn2	159936hf2	159936.jn	159936hf	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{12} \cdot 3^{2} \cdot 7^{8} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$	$3$	$344064$	$1.373671$	$964430272/127449$	$0.84666$	$3.39497$	$[0, 1, 0, -16137, 687735]$	$y^2=x^3+x^2-16137x+687735$	2.6.0.a.1, 4.12.0-2.a.1.1, 168.24.0.?, 204.24.0.?, 952.24.0.?, $\ldots$	$[]$
194208.i3	194208u1	194208.i	194208u	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17^{2} $	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2856$	$48$	$0$	$4.450778175$	$1$	$7$	$516096$	$1.470749$	$964430272/127449$	$0.84666$	$3.43650$	$[0, -1, 0, -23794, -1233056]$	$y^2=x^3-x^2-23794x-1233056$	2.6.0.a.1, 4.12.0-2.a.1.1, 168.24.0.?, 204.24.0.?, 952.24.0.?, $\ldots$	$[(-112, 120)]$
194208.bn3	194208bl1	194208.bn	194208bl	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17^{2} $	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$	$3$	$516096$	$1.470749$	$964430272/127449$	$0.84666$	$3.43650$	$[0, 1, 0, -23794, 1233056]$	$y^2=x^3+x^2-23794x+1233056$	2.6.0.a.1, 4.12.0-2.a.1.1, 168.24.0.?, 204.24.0.?, 952.24.0.?, $\ldots$	$[]$
239904.de3	239904de1	239904.de	239904de	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 3^{8} \cdot 7^{8} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$	$3$	$688128$	$1.576403$	$964430272/127449$	$0.84666$	$3.48023$	$[0, 0, 0, -36309, 2339260]$	$y^2=x^3-36309x+2339260$	2.6.0.a.1, 24.12.0-2.a.1.1, 28.12.0-2.a.1.1, 136.12.0.?, 168.24.0.?, $\ldots$	$[]$
239904.df3	239904df1	239904.df	239904df	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 3^{8} \cdot 7^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$7.580371716$	$1$	$3$	$688128$	$1.576403$	$964430272/127449$	$0.84666$	$3.48023$	$[0, 0, 0, -36309, -2339260]$	$y^2=x^3-36309x-2339260$	2.6.0.a.1, 24.12.0-2.a.1.1, 28.12.0-2.a.1.1, 136.12.0.?, 168.24.0.?, $\ldots$	$[(60529/10, 14051583/10)]$
285600.cr3	285600cr1	285600.cr	285600cr	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$14280$	$48$	$0$	$2.340503621$	$1$	$7$	$229376$	$0.858860$	$964430272/127449$	$0.84666$	$2.74651$	$[0, -1, 0, -2058, -30888]$	$y^2=x^3-x^2-2058x-30888$	2.6.0.a.1, 60.12.0-2.a.1.1, 168.12.0.?, 204.12.0.?, 280.12.0.?, $\ldots$	$[(102, 900)]$
285600.ec3	285600ec1	285600.ec	285600ec	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$14280$	$48$	$0$	$1$	$1$	$3$	$229376$	$0.858860$	$964430272/127449$	$0.84666$	$2.74651$	$[0, 1, 0, -2058, 30888]$	$y^2=x^3+x^2-2058x+30888$	2.6.0.a.1, 60.12.0-2.a.1.1, 168.12.0.?, 204.12.0.?, 280.12.0.?, $\ldots$	$[]$
388416.df2	388416df2	388416.df	388416df	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17^{2} $	$ 2^{12} \cdot 3^{2} \cdot 7^{2} \cdot 17^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2856$	$48$	$0$	$4.829422280$	$1$	$5$	$2064384$	$1.817322$	$964430272/127449$	$0.84666$	$3.57457$	$[0, -1, 0, -95177, 9959625]$	$y^2=x^3-x^2-95177x+9959625$	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 204.12.0.?, $\ldots$	$[(325, 3640)]$
388416.hr2	388416hr2	388416.hr	388416hr	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17^{2} $	$ 2^{12} \cdot 3^{2} \cdot 7^{2} \cdot 17^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2856$	$48$	$0$	$13.84174841$	$1$	$3$	$2064384$	$1.817322$	$964430272/127449$	$0.84666$	$3.57457$	$[0, 1, 0, -95177, -9959625]$	$y^2=x^3+x^2-95177x-9959625$	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 204.12.0.?, $\ldots$	$[(-1998081/113, 1531490400/113)]$
479808.dt2	479808dt2	479808.dt	479808dt	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{12} \cdot 3^{8} \cdot 7^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$2.071182099$	$1$	$11$	$2752512$	$1.922976$	$964430272/127449$	$0.84666$	$3.61375$	$[0, 0, 0, -145236, -18714080]$	$y^2=x^3-145236x-18714080$	2.6.0.a.1, 12.12.0-2.a.1.1, 56.12.0-2.a.1.1, 68.12.0-2.a.1.2, 168.24.0.?, $\ldots$	$[(-252, 1372)]$
479808.dw2	479808dw2	479808.dw	479808dw	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{12} \cdot 3^{8} \cdot 7^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$2.624357339$	$1$	$9$	$2752512$	$1.922976$	$964430272/127449$	$0.84666$	$3.61375$	$[0, 0, 0, -145236, 18714080]$	$y^2=x^3-145236x+18714080$	2.6.0.a.1, 12.12.0-2.a.1.1, 56.12.0-2.a.1.1, 68.12.0-2.a.1.2, 168.24.0.?, $\ldots$	$[(133, 1323)]$

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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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