LMFDB - Elliptic curve search results

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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	Nonmax$\ \ell$	Adelic level	Adelic index	Adelic genus

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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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images
4650.b1	4650m2	4650.b	4650m	$2$	$5$	$ 2 \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{15} \cdot 3^{10} \cdot 5^{8} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.24.0.2	5B.1.4	$1240$	$48$	$1$	$1.016463500$	$1$	$4$	$36000$	$1.825756$	$-12882119799145/59982446592$	$[1, 1, 0, -35700, 7794000]$	$y^2+xy=x^3+x^2-35700x+7794000$	5.24.0-5.a.1.1, 248.2.0.?, 1240.48.1.?
4650.bu2	4650bp1	4650.bu	4650bp	$2$	$5$	$ 2 \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{15} \cdot 3^{10} \cdot 5^{2} \cdot 31 $	$0$	$\Z/5\Z$	$\Q$	$\mathrm{SU}(2)$	$5$	5.24.0.1	5B.1.1	$1240$	$48$	$1$	$1$	$1$	$4$	$7200$	$1.021036$	$-12882119799145/59982446592$	$[1, 0, 0, -1428, 62352]$	$y^2+xy=x^3-1428x+62352$	5.24.0-5.a.1.2, 248.2.0.?, 1240.48.1.?
13950.bk2	13950ba1	13950.bk	13950ba	$2$	$5$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{15} \cdot 3^{16} \cdot 5^{2} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$3720$	$48$	$1$	$5.084089958$	$1$	$0$	$57600$	$1.570343$	$-12882119799145/59982446592$	$[1, -1, 0, -12852, -1683504]$	$y^2+xy=x^3-x^2-12852x-1683504$	5.12.0.a.1, 15.24.0-5.a.1.1, 248.2.0.?, 1240.24.1.?, 3720.48.1.?
13950.bu1	13950dc2	13950.bu	13950dc	$2$	$5$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{15} \cdot 3^{16} \cdot 5^{8} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$3720$	$48$	$1$	$1.255215766$	$1$	$4$	$288000$	$2.375061$	$-12882119799145/59982446592$	$[1, -1, 1, -321305, -210759303]$	$y^2+xy+y=x^3-x^2-321305x-210759303$	5.12.0.a.1, 15.24.0-5.a.1.2, 248.2.0.?, 1240.24.1.?, 3720.48.1.?
37200.i2	37200bo1	37200.i	37200bo	$2$	$5$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{27} \cdot 3^{10} \cdot 5^{2} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$1240$	$48$	$1$	$1$	$1$	$0$	$172800$	$1.714184$	$-12882119799145/59982446592$	$[0, -1, 0, -22848, -3990528]$	$y^2=x^3-x^2-22848x-3990528$	5.12.0.a.1, 20.24.0-5.a.1.2, 248.2.0.?, 1240.48.1.?
37200.du1	37200dr2	37200.du	37200dr	$2$	$5$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{27} \cdot 3^{10} \cdot 5^{8} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$1240$	$48$	$1$	$1$	$1$	$0$	$864000$	$2.518902$	$-12882119799145/59982446592$	$[0, 1, 0, -571208, -499958412]$	$y^2=x^3+x^2-571208x-499958412$	5.12.0.a.1, 20.24.0-5.a.1.1, 248.2.0.?, 1240.48.1.?
111600.bb2	111600ee1	111600.bb	111600ee	$2$	$5$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{27} \cdot 3^{16} \cdot 5^{2} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$3720$	$48$	$1$	$2.758094010$	$1$	$2$	$1382400$	$2.263489$	$-12882119799145/59982446592$	$[0, 0, 0, -205635, 107949890]$	$y^2=x^3-205635x+107949890$	5.12.0.a.1, 60.24.0-5.a.1.2, 248.2.0.?, 1240.24.1.?, 3720.48.1.?
111600.fw1	111600gb2	111600.fw	111600gb	$2$	$5$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{27} \cdot 3^{16} \cdot 5^{8} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$3720$	$48$	$1$	$1$	$1$	$0$	$6912000$	$3.068211$	$-12882119799145/59982446592$	$[0, 0, 0, -5140875, 13493736250]$	$y^2=x^3-5140875x+13493736250$	5.12.0.a.1, 60.24.0-5.a.1.1, 248.2.0.?, 1240.24.1.?, 3720.48.1.?
144150.bp1	144150cr2	144150.bp	144150cr	$2$	$5$	$ 2 \cdot 3 \cdot 5^{2} \cdot 31^{2} $	$ - 2^{15} \cdot 3^{10} \cdot 5^{8} \cdot 31^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$1240$	$48$	$1$	$1$	$1$	$0$	$34560000$	$3.542747$	$-12882119799145/59982446592$	$[1, 0, 1, -34308201, -232637058452]$	$y^2+xy+y=x^3-34308201x-232637058452$	5.12.0.a.1, 40.24.0-5.a.1.8, 155.24.0.?, 248.2.0.?, 1240.48.1.?
144150.dt2	144150ck1	144150.dt	144150ck	$2$	$5$	$ 2 \cdot 3 \cdot 5^{2} \cdot 31^{2} $	$ - 2^{15} \cdot 3^{10} \cdot 5^{2} \cdot 31^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$1240$	$48$	$1$	$3.103315824$	$1$	$2$	$6912000$	$2.738029$	$-12882119799145/59982446592$	$[1, 1, 1, -1372328, -1861645399]$	$y^2+xy+y=x^3+x^2-1372328x-1861645399$	5.12.0.a.1, 40.24.0-5.a.1.7, 155.24.0.?, 248.2.0.?, 1240.48.1.?
148800.ev1	148800dw2	148800.ev	148800dw	$2$	$5$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{33} \cdot 3^{10} \cdot 5^{8} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$1240$	$48$	$1$	$28.64879725$	$1$	$0$	$6912000$	$2.865475$	$-12882119799145/59982446592$	$[0, -1, 0, -2284833, -3997382463]$	$y^2=x^3-x^2-2284833x-3997382463$	5.12.0.a.1, 40.24.0-5.a.1.2, 248.2.0.?, 620.24.0.?, 1240.48.1.?
148800.ez2	148800le1	148800.ez	148800le	$2$	$5$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{33} \cdot 3^{10} \cdot 5^{2} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$1240$	$48$	$1$	$1$	$1$	$0$	$1382400$	$2.060757$	$-12882119799145/59982446592$	$[0, -1, 0, -91393, 32015617]$	$y^2=x^3-x^2-91393x+32015617$	5.12.0.a.1, 40.24.0-5.a.1.3, 248.2.0.?, 310.24.0.?, 1240.48.1.?
148800.gh2	148800bg1	148800.gh	148800bg	$2$	$5$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{33} \cdot 3^{10} \cdot 5^{2} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$1240$	$48$	$1$	$1.205926218$	$1$	$4$	$1382400$	$2.060757$	$-12882119799145/59982446592$	$[0, 1, 0, -91393, -32015617]$	$y^2=x^3+x^2-91393x-32015617$	5.12.0.a.1, 40.24.0-5.a.1.1, 248.2.0.?, 620.24.0.?, 1240.48.1.?
148800.go1	148800fy2	148800.go	148800fy	$2$	$5$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{33} \cdot 3^{10} \cdot 5^{8} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$1240$	$48$	$1$	$1$	$1$	$0$	$6912000$	$2.865475$	$-12882119799145/59982446592$	$[0, 1, 0, -2284833, 3997382463]$	$y^2=x^3+x^2-2284833x+3997382463$	5.12.0.a.1, 40.24.0-5.a.1.4, 248.2.0.?, 310.24.0.?, 1240.48.1.?
227850.dd1	227850ex2	227850.dd	227850ex	$2$	$5$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 31 $	$ - 2^{15} \cdot 3^{10} \cdot 5^{8} \cdot 7^{6} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$8680$	$48$	$1$	$1$	$1$	$0$	$11880000$	$2.798710$	$-12882119799145/59982446592$	$[1, 0, 1, -1749326, -2678589952]$	$y^2+xy+y=x^3-1749326x-2678589952$	5.12.0.a.1, 35.24.0-5.a.1.1, 248.2.0.?, 1240.24.1.?, 8680.48.1.?
227850.fi2	227850do1	227850.fi	227850do	$2$	$5$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 31 $	$ - 2^{15} \cdot 3^{10} \cdot 5^{2} \cdot 7^{6} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$8680$	$48$	$1$	$2.643992174$	$1$	$2$	$2376000$	$1.993992$	$-12882119799145/59982446592$	$[1, 1, 1, -69973, -21456709]$	$y^2+xy+y=x^3+x^2-69973x-21456709$	5.12.0.a.1, 35.24.0-5.a.1.2, 248.2.0.?, 1240.24.1.?, 8680.48.1.?
432450.dd2	432450dd1	432450.dd	432450dd	$2$	$5$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31^{2} $	$ - 2^{15} \cdot 3^{16} \cdot 5^{2} \cdot 31^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$3720$	$48$	$1$	$11.54608226$	$1$	$0$	$55296000$	$3.287338$	$-12882119799145/59982446592$	$[1, -1, 0, -12350952, 50252074816]$	$y^2+xy=x^3-x^2-12350952x+50252074816$	5.12.0.a.1, 120.24.0.?, 248.2.0.?, 465.24.0.?, 1240.24.1.?, $\ldots$
432450.ep1	432450ep2	432450.ep	432450ep	$2$	$5$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31^{2} $	$ - 2^{15} \cdot 3^{16} \cdot 5^{8} \cdot 31^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$3720$	$48$	$1$	$2.304563698$	$1$	$4$	$276480000$	$4.092056$	$-12882119799145/59982446592$	$[1, -1, 1, -308773805, 6281200578197]$	$y^2+xy+y=x^3-x^2-308773805x+6281200578197$	5.12.0.a.1, 120.24.0.?, 248.2.0.?, 465.24.0.?, 1240.24.1.?, $\ldots$
446400.df1	446400df2	446400.df	446400df	$2$	$5$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{33} \cdot 3^{16} \cdot 5^{8} \cdot 31 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$3720$	$48$	$1$	$9.310420677$	$1$	$6$	$55296000$	$3.414783$	$-12882119799145/59982446592$	$[0, 0, 0, -20563500, -107949890000]$	$y^2=x^3-20563500x-107949890000$	5.12.0.a.1, 120.24.0.?, 248.2.0.?, 930.24.0.?, 1240.24.1.?, $\ldots$
446400.dq2	446400dq1	446400.dq	446400dq	$2$	$5$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{33} \cdot 3^{16} \cdot 5^{2} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$3720$	$48$	$1$	$6.910271449$	$1$	$0$	$11059200$	$2.610065$	$-12882119799145/59982446592$	$[0, 0, 0, -822540, 863599120]$	$y^2=x^3-822540x+863599120$	5.12.0.a.1, 120.24.0.?, 248.2.0.?, 1240.24.1.?, 1860.24.0.?, $\ldots$
446400.qc2	446400qc1	446400.qc	446400qc	$2$	$5$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{33} \cdot 3^{16} \cdot 5^{2} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$3720$	$48$	$1$	$17.30269914$	$1$	$0$	$11059200$	$2.610065$	$-12882119799145/59982446592$	$[0, 0, 0, -822540, -863599120]$	$y^2=x^3-822540x-863599120$	5.12.0.a.1, 120.24.0.?, 248.2.0.?, 930.24.0.?, 1240.24.1.?, $\ldots$
446400.qr1	446400qr2	446400.qr	446400qr	$2$	$5$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{33} \cdot 3^{16} \cdot 5^{8} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$3720$	$48$	$1$	$1$	$1$	$0$	$55296000$	$3.414783$	$-12882119799145/59982446592$	$[0, 0, 0, -20563500, 107949890000]$	$y^2=x^3-20563500x+107949890000$	5.12.0.a.1, 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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