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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
11424.j2	11424c2	11424.j	11424c	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{12} \cdot 3 \cdot 7^{4} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$1$	$1$		$1$	$3584$	$0.400715$	$1036433728/122451$	$0.84708$	$3.11199$	$[0, -1, 0, -337, -2015]$	$y^2=x^3-x^2-337x-2015$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 56.12.0-4.c.1.4, 68.12.0-4.c.1.1, $\ldots$	$[]$
11424.s2	11424r3	11424.s	11424r	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{12} \cdot 3 \cdot 7^{4} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$1.863592226$	$1$		$3$	$3584$	$0.400715$	$1036433728/122451$	$0.84708$	$3.11199$	$[0, 1, 0, -337, 2015]$	$y^2=x^3+x^2-337x+2015$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 56.12.0-4.c.1.4, 68.12.0-4.c.1.2, $\ldots$	$[(-5, 60)]$
22848.h3	22848b1	22848.h	22848b	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3 \cdot 7^{4} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$3.177042330$	$1$		$3$	$3584$	$0.054141$	$1036433728/122451$	$0.84708$	$2.48270$	$[0, -1, 0, -84, 294]$	$y^2=x^3-x^2-84x+294$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 56.12.0-4.c.1.5, 136.12.0.?, $\ldots$	$[(23, 100)]$
22848.bv3	22848bh1	22848.bv	22848bh	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3 \cdot 7^{4} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$3.541636146$	$1$		$3$	$3584$	$0.054141$	$1036433728/122451$	$0.84708$	$2.48270$	$[0, 1, 0, -84, -294]$	$y^2=x^3+x^2-84x-294$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 56.12.0-4.c.1.5, 136.12.0.?, $\ldots$	$[(29, 150)]$
34272.h2	34272n3	34272.h	34272n	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 17 $	$ 2^{12} \cdot 3^{7} \cdot 7^{4} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$2856$	$48$	$0$	$2.959835603$	$1$		$3$	$28672$	$0.950021$	$1036433728/122451$	$0.84708$	$3.41584$	$[0, 0, 0, -3036, -57440]$	$y^2=x^3-3036x-57440$	2.3.0.a.1, 4.12.0-4.c.1.2, 168.24.0.?, 204.24.0.?, 952.24.0.?, $\ldots$	$[(-24, 40)]$
34272.k2	34272bm3	34272.k	34272bm	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 17 $	$ 2^{12} \cdot 3^{7} \cdot 7^{4} \cdot 17 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$2856$	$48$	$0$	$1.353917254$	$1$		$13$	$28672$	$0.950021$	$1036433728/122451$	$0.84708$	$3.41584$	$[0, 0, 0, -3036, 57440]$	$y^2=x^3-3036x+57440$	2.3.0.a.1, 4.12.0-4.c.1.1, 168.24.0.?, 204.24.0.?, 952.24.0.?, $\ldots$	$[(22, 36)]$
68544.dq3	68544bl1	68544.dq	68544bl	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{7} \cdot 7^{4} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$2856$	$48$	$0$	$4.365597619$	$1$		$1$	$28672$	$0.603448$	$1036433728/122451$	$0.84708$	$2.82972$	$[0, 0, 0, -759, -7180]$	$y^2=x^3-759x-7180$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 168.24.0.?, 204.12.0.?, $\ldots$	$[(-55/2, 205/2)]$
68544.eh3	68544cl1	68544.eh	68544cl	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{7} \cdot 7^{4} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$2856$	$48$	$0$	$1$	$1$		$1$	$28672$	$0.603448$	$1036433728/122451$	$0.84708$	$2.82972$	$[0, 0, 0, -759, 7180]$	$y^2=x^3-759x+7180$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 168.24.0.?, 204.12.0.?, $\ldots$	$[]$
79968.i2	79968bw3	79968.i	79968bw	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{12} \cdot 3 \cdot 7^{10} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$2856$	$48$	$0$	$1$	$1$		$1$	$172032$	$1.373671$	$1036433728/122451$	$0.84708$	$3.60979$	$[0, -1, 0, -16529, -724191]$	$y^2=x^3-x^2-16529x-724191$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 84.12.0.?, 168.24.0.?, $\ldots$	$[]$
79968.bu2	79968bd3	79968.bu	79968bd	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{12} \cdot 3 \cdot 7^{10} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$2856$	$48$	$0$	$1$	$1$		$1$	$172032$	$1.373671$	$1036433728/122451$	$0.84708$	$3.60979$	$[0, 1, 0, -16529, 724191]$	$y^2=x^3+x^2-16529x+724191$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 84.12.0.?, 168.24.0.?, $\ldots$	$[]$
159936.dz3	159936jz1	159936.dz	159936jz	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 3 \cdot 7^{10} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$2856$	$48$	$0$	$8.707729345$	$1$		$1$	$172032$	$1.027096$	$1036433728/122451$	$0.84708$	$3.05390$	$[0, -1, 0, -4132, 92590]$	$y^2=x^3-x^2-4132x+92590$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 168.24.0.?, 204.12.0.?, $\ldots$	$[(5787/11, 60710/11)]$
159936.jn3	159936hf1	159936.jn	159936hf	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 3 \cdot 7^{10} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$2856$	$48$	$0$	$1$	$4$	$2$	$1$	$172032$	$1.027096$	$1036433728/122451$	$0.84708$	$3.05390$	$[0, 1, 0, -4132, -92590]$	$y^2=x^3+x^2-4132x-92590$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 168.24.0.?, 204.12.0.?, $\ldots$	$[]$
194208.i2	194208u2	194208.i	194208u	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17^{2} $	$ 2^{12} \cdot 3 \cdot 7^{4} \cdot 17^{7} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$2856$	$48$	$0$	$2.225389087$	$1$		$9$	$1032192$	$1.817322$	$1036433728/122451$	$0.84708$	$3.78396$	$[0, -1, 0, -97489, 10484449]$	$y^2=x^3-x^2-97489x+10484449$	2.3.0.a.1, 4.12.0-4.c.1.1, 168.24.0.?, 204.24.0.?, 952.24.0.?, $\ldots$	$[(129, 196)]$
194208.bn2	194208bl4	194208.bn	194208bl	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17^{2} $	$ 2^{12} \cdot 3 \cdot 7^{4} \cdot 17^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$2856$	$48$	$0$	$1$	$1$		$1$	$1032192$	$1.817322$	$1036433728/122451$	$0.84708$	$3.78396$	$[0, 1, 0, -97489, -10484449]$	$y^2=x^3+x^2-97489x-10484449$	2.3.0.a.1, 4.12.0-4.c.1.2, 168.24.0.?, 204.24.0.?, 952.24.0.?, $\ldots$	$[]$
239904.de2	239904de4	239904.de	239904de	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{12} \cdot 3^{7} \cdot 7^{10} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$1$	$1$		$1$	$1376256$	$1.922976$	$1036433728/122451$	$0.84708$	$3.82176$	$[0, 0, 0, -148764, -19701920]$	$y^2=x^3-148764x-19701920$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.6, 28.12.0-4.c.1.2, 136.12.0.?, $\ldots$	$[]$
239904.df2	239904df2	239904.df	239904df	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{12} \cdot 3^{7} \cdot 7^{10} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$3.790185858$	$1$		$3$	$1376256$	$1.922976$	$1036433728/122451$	$0.84708$	$3.82176$	$[0, 0, 0, -148764, 19701920]$	$y^2=x^3-148764x+19701920$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.6, 28.12.0-4.c.1.1, 136.12.0.?, $\ldots$	$[(2380, 114660)]$
285600.cr2	285600cr2	285600.cr	285600cr	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $	$ 2^{12} \cdot 3 \cdot 5^{6} \cdot 7^{4} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$14280$	$48$	$0$	$1.170251810$	$1$		$5$	$458752$	$1.205435$	$1036433728/122451$	$0.84708$	$3.08330$	$[0, -1, 0, -8433, 268737]$	$y^2=x^3-x^2-8433x+268737$	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.1, 168.12.0.?, 204.12.0.?, $\ldots$	$[(32, 175)]$
285600.ec2	285600ec4	285600.ec	285600ec	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $	$ 2^{12} \cdot 3 \cdot 5^{6} \cdot 7^{4} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$14280$	$48$	$0$	$1$	$1$		$1$	$458752$	$1.205435$	$1036433728/122451$	$0.84708$	$3.08330$	$[0, 1, 0, -8433, -268737]$	$y^2=x^3+x^2-8433x-268737$	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.2, 168.12.0.?, 204.12.0.?, $\ldots$	$[]$
388416.df3	388416df1	388416.df	388416df	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17^{2} $	$ 2^{6} \cdot 3 \cdot 7^{4} \cdot 17^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$2856$	$48$	$0$	$9.658844561$	$1$		$1$	$1032192$	$1.470749$	$1036433728/122451$	$0.84708$	$3.25701$	$[0, -1, 0, -24372, -1298370]$	$y^2=x^3-x^2-24372x-1298370$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 168.24.0.?, 204.12.0.?, $\ldots$	$[(11363/7, 801970/7)]$
388416.hr3	388416hr1	388416.hr	388416hr	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17^{2} $	$ 2^{6} \cdot 3 \cdot 7^{4} \cdot 17^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$2856$	$48$	$0$	$6.920874209$	$1$		$1$	$1032192$	$1.470749$	$1036433728/122451$	$0.84708$	$3.25701$	$[0, 1, 0, -24372, 1298370]$	$y^2=x^3+x^2-24372x+1298370$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 168.24.0.?, 204.12.0.?, $\ldots$	$[(72073/36, 16032275/36)]$
479808.dt3	479808dt1	479808.dt	479808dt	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 3^{7} \cdot 7^{10} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$4.142364198$	$1$		$3$	$1376256$	$1.576403$	$1036433728/122451$	$0.84708$	$3.30132$	$[0, 0, 0, -37191, 2462740]$	$y^2=x^3-37191x+2462740$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 56.12.0-4.c.1.2, 136.12.0.?, $\ldots$	$[(176, 1170)]$
479808.dw3	479808dw1	479808.dw	479808dw	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 3^{7} \cdot 7^{10} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$5.248714679$	$1$		$1$	$1376256$	$1.576403$	$1036433728/122451$	$0.84708$	$3.30132$	$[0, 0, 0, -37191, -2462740]$	$y^2=x^3-37191x-2462740$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 56.12.0-4.c.1.1, 136.12.0.?, $\ldots$	$[(-479/2, 4185/2)]$

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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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