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
4650.b2	4650m1	4650.b	4650m	$2$	$5$	$ 2 \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{3} \cdot 3^{2} \cdot 5^{4} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.24.0.4	5B.1.3	$1240$	$48$	$1$	$0.203292700$	$1$	$6$	$7200$	$1.021036$	$-2372030262025/2061298872$	$0.98149$	$4.24524$	$[1, 1, 0, -2375, -71475]$	$y^2+xy=x^3+x^2-2375x-71475$	5.24.0-5.a.2.1, 248.2.0.?, 1240.48.1.?	$[(65, 200)]$
4650.bu1	4650bp2	4650.bu	4650bp	$2$	$5$	$ 2 \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{3} \cdot 3^{2} \cdot 5^{10} \cdot 31^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.24.0.3	5B.1.2	$1240$	$48$	$1$	$1$	$1$	$0$	$36000$	$1.825756$	$-2372030262025/2061298872$	$0.98149$	$5.38877$	$[1, 0, 0, -59388, -8815608]$	$y^2+xy=x^3-59388x-8815608$	5.24.0-5.a.2.2, 248.2.0.?, 1240.48.1.?	$[]$
13950.bk1	13950ba2	13950.bk	13950ba	$2$	$5$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{3} \cdot 3^{8} \cdot 5^{10} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3720$	$48$	$1$	$1.016817991$	$1$	$4$	$288000$	$2.375061$	$-2372030262025/2061298872$	$0.98149$	$5.45913$	$[1, -1, 0, -534492, 238021416]$	$y^2+xy=x^3-x^2-534492x+238021416$	5.12.0.a.2, 15.24.0-5.a.2.1, 248.2.0.?, 1240.24.1.?, 3720.48.1.?	$[(135, 12906)]$
13950.bu2	13950dc1	13950.bu	13950dc	$2$	$5$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{3} \cdot 3^{8} \cdot 5^{4} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3720$	$48$	$1$	$0.251043153$	$1$	$6$	$57600$	$1.570343$	$-2372030262025/2061298872$	$0.98149$	$4.44725$	$[1, -1, 1, -21380, 1908447]$	$y^2+xy+y=x^3-x^2-21380x+1908447$	5.12.0.a.2, 15.24.0-5.a.2.2, 248.2.0.?, 1240.24.1.?, 3720.48.1.?	$[(83, 795)]$
37200.i1	37200bo2	37200.i	37200bo	$2$	$5$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{15} \cdot 3^{2} \cdot 5^{10} \cdot 31^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$1240$	$48$	$1$	$1$	$1$	$0$	$864000$	$2.518902$	$-2372030262025/2061298872$	$0.98149$	$5.11436$	$[0, -1, 0, -950208, 564198912]$	$y^2=x^3-x^2-950208x+564198912$	5.12.0.a.2, 20.24.0-5.a.2.2, 248.2.0.?, 1240.48.1.?	$[]$
37200.du2	37200dr1	37200.du	37200dr	$2$	$5$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{15} \cdot 3^{2} \cdot 5^{4} \cdot 31^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$1240$	$48$	$1$	$1$	$1$	$0$	$172800$	$1.714184$	$-2372030262025/2061298872$	$0.98149$	$4.19678$	$[0, 1, 0, -38008, 4498388]$	$y^2=x^3+x^2-38008x+4498388$	5.12.0.a.2, 20.24.0-5.a.2.1, 248.2.0.?, 1240.48.1.?	$[]$
111600.bb1	111600ee2	111600.bb	111600ee	$2$	$5$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{15} \cdot 3^{8} \cdot 5^{10} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3720$	$48$	$1$	$13.79047005$	$1$	$0$	$6912000$	$3.068211$	$-2372030262025/2061298872$	$0.98149$	$5.19807$	$[0, 0, 0, -8551875, -15224818750]$	$y^2=x^3-8551875x-15224818750$	5.12.0.a.2, 60.24.0-5.a.2.2, 248.2.0.?, 1240.24.1.?, 3720.48.1.?	$[(4080814/23, 7479177012/23)]$
111600.fw2	111600gb1	111600.fw	111600gb	$2$	$5$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{15} \cdot 3^{8} \cdot 5^{4} \cdot 31^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3720$	$48$	$1$	$1$	$1$	$0$	$1382400$	$2.263489$	$-2372030262025/2061298872$	$0.98149$	$4.36723$	$[0, 0, 0, -342075, -121798550]$	$y^2=x^3-342075x-121798550$	5.12.0.a.2, 60.24.0-5.a.2.1, 248.2.0.?, 1240.24.1.?, 3720.48.1.?	$[]$
144150.bp2	144150cr1	144150.bp	144150cr	$2$	$5$	$ 2 \cdot 3 \cdot 5^{2} \cdot 31^{2} $	$ - 2^{3} \cdot 3^{2} \cdot 5^{4} \cdot 31^{11} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$1240$	$48$	$1$	$1$	$1$	$0$	$6912000$	$2.738029$	$-2372030262025/2061298872$	$0.98149$	$4.75252$	$[1, 0, 1, -2282876, 2099636498]$	$y^2+xy+y=x^3-2282876x+2099636498$	5.12.0.a.2, 40.24.0-5.a.2.8, 155.24.0.?, 248.2.0.?, 1240.48.1.?	$[]$
144150.dt1	144150ck2	144150.dt	144150ck	$2$	$5$	$ 2 \cdot 3 \cdot 5^{2} \cdot 31^{2} $	$ - 2^{3} \cdot 3^{2} \cdot 5^{10} \cdot 31^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$1240$	$48$	$1$	$15.51657912$	$1$	$0$	$34560000$	$3.542747$	$-2372030262025/2061298872$	$0.98149$	$5.56547$	$[1, 1, 1, -57071888, 262454562281]$	$y^2+xy+y=x^3+x^2-57071888x+262454562281$	5.12.0.a.2, 40.24.0-5.a.2.7, 155.24.0.?, 248.2.0.?, 1240.48.1.?	$[(-6558369/35, 27721249991/35)]$
148800.ev2	148800dw1	148800.ev	148800dw	$2$	$5$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{21} \cdot 3^{2} \cdot 5^{4} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$1240$	$48$	$1$	$5.729759451$	$1$	$2$	$1382400$	$2.060757$	$-2372030262025/2061298872$	$0.98149$	$4.05749$	$[0, -1, 0, -152033, 36139137]$	$y^2=x^3-x^2-152033x+36139137$	5.12.0.a.2, 40.24.0-5.a.2.2, 248.2.0.?, 620.24.0.?, 1240.48.1.?	$[(-64, 6753)]$
148800.ez1	148800le2	148800.ez	148800le	$2$	$5$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{21} \cdot 3^{2} \cdot 5^{10} \cdot 31^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$1240$	$48$	$1$	$1$	$1$	$0$	$6912000$	$2.865475$	$-2372030262025/2061298872$	$0.98149$	$4.86826$	$[0, -1, 0, -3800833, -4509790463]$	$y^2=x^3-x^2-3800833x-4509790463$	5.12.0.a.2, 40.24.0-5.a.2.3, 248.2.0.?, 310.24.0.?, 1240.48.1.?	$[]$
148800.gh1	148800bg2	148800.gh	148800bg	$2$	$5$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{21} \cdot 3^{2} \cdot 5^{10} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$1240$	$48$	$1$	$6.029631094$	$1$	$2$	$6912000$	$2.865475$	$-2372030262025/2061298872$	$0.98149$	$4.86826$	$[0, 1, 0, -3800833, 4509790463]$	$y^2=x^3+x^2-3800833x+4509790463$	5.12.0.a.2, 40.24.0-5.a.2.1, 248.2.0.?, 620.24.0.?, 1240.48.1.?	$[(4927, 324672)]$
148800.go2	148800fy1	148800.go	148800fy	$2$	$5$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{21} \cdot 3^{2} \cdot 5^{4} \cdot 31^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$1240$	$48$	$1$	$1$	$1$	$0$	$1382400$	$2.060757$	$-2372030262025/2061298872$	$0.98149$	$4.05749$	$[0, 1, 0, -152033, -36139137]$	$y^2=x^3+x^2-152033x-36139137$	5.12.0.a.2, 40.24.0-5.a.2.4, 248.2.0.?, 310.24.0.?, 1240.48.1.?	$[]$
227850.dd2	227850ex1	227850.dd	227850ex	$2$	$5$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 31 $	$ - 2^{3} \cdot 3^{2} \cdot 5^{4} \cdot 7^{6} \cdot 31^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$8680$	$48$	$1$	$1$	$1$	$0$	$2376000$	$1.993992$	$-2372030262025/2061298872$	$0.98149$	$3.85240$	$[1, 0, 1, -116401, 24166748]$	$y^2+xy+y=x^3-116401x+24166748$	5.12.0.a.2, 35.24.0-5.a.2.1, 248.2.0.?, 1240.24.1.?, 8680.48.1.?	$[]$
227850.fi1	227850do2	227850.fi	227850do	$2$	$5$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 31 $	$ - 2^{3} \cdot 3^{2} \cdot 5^{10} \cdot 7^{6} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$8680$	$48$	$1$	$13.21996087$	$1$	$0$	$11880000$	$2.798710$	$-2372030262025/2061298872$	$0.98149$	$4.63517$	$[1, 1, 1, -2910013, 3020843531]$	$y^2+xy+y=x^3+x^2-2910013x+3020843531$	5.12.0.a.2, 35.24.0-5.a.2.2, 248.2.0.?, 1240.24.1.?, 8680.48.1.?	$[(553679/22, 361311645/22)]$
432450.dd1	432450dd2	432450.dd	432450dd	$2$	$5$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31^{2} $	$ - 2^{3} \cdot 3^{8} \cdot 5^{10} \cdot 31^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3720$	$48$	$1$	$57.73041134$	$1$	$0$	$276480000$	$4.092056$	$-2372030262025/2061298872$	$0.98149$	$5.60225$	$[1, -1, 0, -513646992, -7086786828584]$	$y^2+xy=x^3-x^2-513646992x-7086786828584$	5.12.0.a.2, 120.24.0.?, 248.2.0.?, 465.24.0.?, 1240.24.1.?, $\ldots$	$[(1410218915355232312762588157/183858715117, 41137745022236586328611974680287393647564/183858715117)]$
432450.ep2	432450ep1	432450.ep	432450ep	$2$	$5$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31^{2} $	$ - 2^{3} \cdot 3^{8} \cdot 5^{4} \cdot 31^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3720$	$48$	$1$	$11.52281849$	$1$	$0$	$55296000$	$3.287338$	$-2372030262025/2061298872$	$0.98149$	$4.85813$	$[1, -1, 1, -20545880, -56690185453]$	$y^2+xy+y=x^3-x^2-20545880x-56690185453$	5.12.0.a.2, 120.24.0.?, 248.2.0.?, 465.24.0.?, 1240.24.1.?, $\ldots$	$[(16981479/55, 11127628507/55)]$
446400.df2	446400df1	446400.df	446400df	$2$	$5$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{21} \cdot 3^{8} \cdot 5^{4} \cdot 31^{5} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3720$	$48$	$1$	$0.372416827$	$1$	$20$	$11059200$	$2.610065$	$-2372030262025/2061298872$	$0.98149$	$4.22153$	$[0, 0, 0, -1368300, 974388400]$	$y^2=x^3-1368300x+974388400$	5.12.0.a.2, 120.24.0.?, 248.2.0.?, 930.24.0.?, 1240.24.1.?, $\ldots$	$[(2150, 89280), (14054, 1660608)]$
446400.dq1	446400dq2	446400.dq	446400dq	$2$	$5$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{21} \cdot 3^{8} \cdot 5^{10} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3720$	$48$	$1$	$34.55135724$	$1$	$0$	$55296000$	$3.414783$	$-2372030262025/2061298872$	$0.98149$	$4.96384$	$[0, 0, 0, -34207500, -121798550000]$	$y^2=x^3-34207500x-121798550000$	5.12.0.a.2, 120.24.0.?, 248.2.0.?, 1240.24.1.?, 1860.24.0.?, $\ldots$	$[(7481654238358976/899815, 431695466906697305393724/899815)]$
446400.qc1	446400qc2	446400.qc	446400qc	$2$	$5$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{21} \cdot 3^{8} \cdot 5^{10} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3720$	$48$	$1$	$3.460539828$	$1$	$2$	$55296000$	$3.414783$	$-2372030262025/2061298872$	$0.98149$	$4.96384$	$[0, 0, 0, -34207500, 121798550000]$	$y^2=x^3-34207500x+121798550000$	5.12.0.a.2, 120.24.0.?, 248.2.0.?, 930.24.0.?, 1240.24.1.?, $\ldots$	$[(18376, 2387124)]$
446400.qr2	446400qr1	446400.qr	446400qr	$2$	$5$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{21} \cdot 3^{8} \cdot 5^{4} \cdot 31^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3720$	$48$	$1$	$1$	$1$	$0$	$11059200$	$2.610065$	$-2372030262025/2061298872$	$0.98149$	$4.22153$	$[0, 0, 0, -1368300, -974388400]$	$y^2=x^3-1368300x-974388400$	5.12.0.a.2, 120.24.0.?, 248.2.0.?, 1240.24.1.?, 1860.24.0.?, $\ldots$	$[]$

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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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