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 (20 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
7098.k4	7098o2	7098.k	7098o	$4$	$10$	$ 2 \cdot 3 \cdot 7 \cdot 13^{2} $	$ - 2 \cdot 3^{10} \cdot 7^{2} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$1$	$1$		$0$	$62400$	$1.907375$	$-1680914269/5786802$	$1.04977$	$5.21741$	$[1, 0, 1, -54422, -12885910]$	$y^2+xy+y=x^3-54422x-12885910$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.24.0-65.a.2.3, $\ldots$	$[]$
7098.bc4	7098y2	7098.bc	7098y	$4$	$10$	$ 2 \cdot 3 \cdot 7 \cdot 13^{2} $	$ - 2 \cdot 3^{10} \cdot 7^{2} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$1$	$1$		$0$	$4800$	$0.624901$	$-1680914269/5786802$	$1.04977$	$3.48191$	$[1, 0, 0, -322, -5890]$	$y^2+xy=x^3-322x-5890$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.24.0-65.a.2.2, $\ldots$	$[]$
21294.f4	21294z2	21294.f	21294z	$4$	$10$	$ 2 \cdot 3^{2} \cdot 7 \cdot 13^{2} $	$ - 2 \cdot 3^{16} \cdot 7^{2} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$1.097271045$	$1$		$6$	$38400$	$1.174206$	$-1680914269/5786802$	$1.04977$	$3.75949$	$[1, -1, 0, -2898, 159030]$	$y^2+xy=x^3-x^2-2898x+159030$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.12.0.a.2, $\ldots$	$[(-3, 411)]$
21294.cp4	21294cv2	21294.cp	21294cv	$4$	$10$	$ 2 \cdot 3^{2} \cdot 7 \cdot 13^{2} $	$ - 2 \cdot 3^{16} \cdot 7^{2} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$13.10054408$	$1$		$0$	$499200$	$2.456680$	$-1680914269/5786802$	$1.04977$	$5.30368$	$[1, -1, 1, -489794, 347919563]$	$y^2+xy+y=x^3-x^2-489794x+347919563$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.12.0.a.2, $\ldots$	$[(7937469/148, 47266448323/148)]$
49686.s4	49686v2	49686.s	49686v	$4$	$10$	$ 2 \cdot 3 \cdot 7^{2} \cdot 13^{2} $	$ - 2 \cdot 3^{10} \cdot 7^{8} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$9.557712130$	$1$		$0$	$2995200$	$2.880329$	$-1680914269/5786802$	$1.04977$	$5.35824$	$[1, 1, 0, -2666654, 4417200390]$	$y^2+xy=x^3+x^2-2666654x+4417200390$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.12.0.a.2, $\ldots$	$[(-16221/10, 69690897/10)]$
49686.bx4	49686cp2	49686.bx	49686cp	$4$	$10$	$ 2 \cdot 3 \cdot 7^{2} \cdot 13^{2} $	$ - 2 \cdot 3^{10} \cdot 7^{8} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$1$	$1$		$0$	$230400$	$1.597857$	$-1680914269/5786802$	$1.04977$	$3.93504$	$[1, 1, 1, -15779, 2004491]$	$y^2+xy+y=x^3+x^2-15779x+2004491$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.12.0.a.2, $\ldots$	$[]$
56784.f4	56784bq2	56784.f	56784bq	$4$	$10$	$ 2^{4} \cdot 3 \cdot 7 \cdot 13^{2} $	$ - 2^{13} \cdot 3^{10} \cdot 7^{2} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$3.055619354$	$1$		$3$	$1497600$	$2.600521$	$-1680914269/5786802$	$1.04977$	$4.98616$	$[0, -1, 0, -870744, 824698224]$	$y^2=x^3-x^2-870744x+824698224$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.12.0.a.2, $\ldots$	$[(948, 29160)]$
56784.bj4	56784cg2	56784.bj	56784cg	$4$	$10$	$ 2^{4} \cdot 3 \cdot 7 \cdot 13^{2} $	$ - 2^{13} \cdot 3^{10} \cdot 7^{2} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$1$	$1$		$1$	$115200$	$1.318048$	$-1680914269/5786802$	$1.04977$	$3.58032$	$[0, -1, 0, -5152, 376960]$	$y^2=x^3-x^2-5152x+376960$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.12.0.a.2, $\ldots$	$[]$
149058.dh4	149058gh2	149058.dh	149058gh	$4$	$10$	$ 2 \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} $	$ - 2 \cdot 3^{16} \cdot 7^{8} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$1$	$1$		$0$	$1843200$	$2.147163$	$-1680914269/5786802$	$1.04977$	$4.12549$	$[1, -1, 0, -142011, -54263273]$	$y^2+xy=x^3-x^2-142011x-54263273$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.12.0.a.2, $\ldots$	$[]$
149058.fk4	149058s2	149058.fk	149058s	$4$	$10$	$ 2 \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} $	$ - 2 \cdot 3^{16} \cdot 7^{8} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$37.62202816$	$1$		$0$	$23961600$	$3.429638$	$-1680914269/5786802$	$1.04977$	$5.41743$	$[1, -1, 1, -23999891, -119288410419]$	$y^2+xy+y=x^3-x^2-23999891x-119288410419$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.12.0.a.2, $\ldots$	$[(259271489643723111/6309850, 5046012611308579209825591/6309850)]$
170352.bs4	170352q2	170352.bs	170352q	$4$	$10$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 13^{2} $	$ - 2^{13} \cdot 3^{16} \cdot 7^{2} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$2.468481375$	$1$		$5$	$921600$	$1.867353$	$-1680914269/5786802$	$1.04977$	$3.80101$	$[0, 0, 0, -46371, -10131550]$	$y^2=x^3-46371x-10131550$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.12.0.a.2, $\ldots$	$[(377, 5096)]$
170352.ev4	170352ci2	170352.ev	170352ci	$4$	$10$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 13^{2} $	$ - 2^{13} \cdot 3^{16} \cdot 7^{2} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$1$	$9$	$3$	$1$	$11980800$	$3.149830$	$-1680914269/5786802$	$1.04977$	$5.07862$	$[0, 0, 0, -7836699, -22259015350]$	$y^2=x^3-7836699x-22259015350$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.12.0.a.2, $\ldots$	$[]$
177450.bw4	177450iw2	177450.bw	177450iw	$4$	$10$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13^{2} $	$ - 2 \cdot 3^{10} \cdot 5^{6} \cdot 7^{2} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$2.415576486$	$1$		$4$	$614400$	$1.429619$	$-1680914269/5786802$	$1.04977$	$3.35356$	$[1, 1, 0, -8050, -736250]$	$y^2+xy=x^3+x^2-8050x-736250$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.24.0-65.a.2.1, $\ldots$	$[(135, 745)]$
177450.fy4	177450ew2	177450.fy	177450ew	$4$	$10$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13^{2} $	$ - 2 \cdot 3^{10} \cdot 5^{6} \cdot 7^{2} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$15.48299437$	$1$		$0$	$7987200$	$2.712093$	$-1680914269/5786802$	$1.04977$	$4.62687$	$[1, 1, 1, -1360538, -1610738719]$	$y^2+xy+y=x^3+x^2-1360538x-1610738719$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.24.0-65.a.2.4, $\ldots$	$[(1135119035/358, 37665551518879/358)]$
227136.v4	227136hq2	227136.v	227136hq	$4$	$10$	$ 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} $	$ - 2^{19} \cdot 3^{10} \cdot 7^{2} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$1$	$1$		$1$	$921600$	$1.664621$	$-1680914269/5786802$	$1.04977$	$3.51509$	$[0, -1, 0, -20609, -2995071]$	$y^2=x^3-x^2-20609x-2995071$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.12.0.a.2, $\ldots$	$[]$
227136.dx4	227136iu2	227136.dx	227136iu	$4$	$10$	$ 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} $	$ - 2^{19} \cdot 3^{10} \cdot 7^{2} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$22.45162489$	$1$		$1$	$11980800$	$2.947098$	$-1680914269/5786802$	$1.04977$	$4.76291$	$[0, -1, 0, -3482977, -6594102815]$	$y^2=x^3-x^2-3482977x-6594102815$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.12.0.a.2, $\ldots$	$[(2173342066729/5249, 3203058509043372000/5249)]$
227136.gb4	227136j2	227136.gb	227136j	$4$	$10$	$ 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} $	$ - 2^{19} \cdot 3^{10} \cdot 7^{2} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$0.531728642$	$1$		$9$	$921600$	$1.664621$	$-1680914269/5786802$	$1.04977$	$3.51509$	$[0, 1, 0, -20609, 2995071]$	$y^2=x^3+x^2-20609x+2995071$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.12.0.a.2, $\ldots$	$[(-65, 2016)]$
227136.ic4	227136bw2	227136.ic	227136bw	$4$	$10$	$ 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} $	$ - 2^{19} \cdot 3^{10} \cdot 7^{2} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$1$	$1$		$1$	$11980800$	$2.947098$	$-1680914269/5786802$	$1.04977$	$4.76291$	$[0, 1, 0, -3482977, 6594102815]$	$y^2=x^3+x^2-3482977x+6594102815$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.12.0.a.2, $\ldots$	$[]$
397488.gk4	397488gk2	397488.gk	397488gk	$4$	$10$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 13^{2} $	$ - 2^{13} \cdot 3^{10} \cdot 7^{8} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$1.927265724$	$1$		$5$	$5529600$	$2.291004$	$-1680914269/5786802$	$1.04977$	$3.94552$	$[0, 1, 0, -252464, -128792364]$	$y^2=x^3+x^2-252464x-128792364$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.12.0.a.2, $\ldots$	$[(1108, 30870)]$
397488.jb4	397488jb2	397488.jb	397488jb	$4$	$10$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 13^{2} $	$ - 2^{13} \cdot 3^{10} \cdot 7^{8} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10920$	$288$	$5$	$5.277679219$	$1$		$3$	$71884800$	$3.573479$	$-1680914269/5786802$	$1.04977$	$5.13917$	$[0, 1, 0, -42666472, -282786157900]$	$y^2=x^3+x^2-42666472x-282786157900$	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 40.36.0.f.2, 65.12.0.a.2, $\ldots$	$[(168758, 69272280)]$

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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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