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
31200.z2	31200l1	31200.z	31200l	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{6} \cdot 3^{2} \cdot 5^{3} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$		$1$	$7168$	$0.061373$	$107850176/117$	$1.01593$	$2.65587$	$[0, -1, 0, -198, -1008]$	$y^2=x^3-x^2-198x-1008$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[]$
31200.bd2	31200bt1	31200.bd	31200bt	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{6} \cdot 3^{2} \cdot 5^{9} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$		$1$	$35840$	$0.866092$	$107850176/117$	$1.01593$	$3.58905$	$[0, -1, 0, -4958, 135912]$	$y^2=x^3-x^2-4958x+135912$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[]$
31200.bg2	31200cj1	31200.bg	31200cj	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{6} \cdot 3^{2} \cdot 5^{9} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$4.983758325$	$1$		$3$	$35840$	$0.866092$	$107850176/117$	$1.01593$	$3.58905$	$[0, 1, 0, -4958, -135912]$	$y^2=x^3+x^2-4958x-135912$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[(3958, 249000)]$
31200.bk2	31200ba1	31200.bk	31200ba	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{6} \cdot 3^{2} \cdot 5^{3} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1.055632380$	$1$		$5$	$7168$	$0.061373$	$107850176/117$	$1.01593$	$2.65587$	$[0, 1, 0, -198, 1008]$	$y^2=x^3+x^2-198x+1008$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[(9, 6)]$
62400.i2	62400fy1	62400.i	62400fy	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{12} \cdot 3^{2} \cdot 5^{3} \cdot 13 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1.006680321$	$1$		$19$	$28672$	$0.407947$	$107850176/117$	$1.01593$	$2.86581$	$[0, -1, 0, -793, 8857]$	$y^2=x^3-x^2-793x+8857$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[(7, 60), (16, 3)]$
62400.p2	62400fr1	62400.p	62400fr	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{12} \cdot 3^{2} \cdot 5^{9} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$2.405957461$	$1$		$5$	$143360$	$1.212666$	$107850176/117$	$1.01593$	$3.74040$	$[0, -1, 0, -19833, -1067463]$	$y^2=x^3-x^2-19833x-1067463$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[(-79, 8)]$
62400.hr2	62400hv1	62400.hr	62400hv	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{12} \cdot 3^{2} \cdot 5^{9} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$		$1$	$143360$	$1.212666$	$107850176/117$	$1.01593$	$3.74040$	$[0, 1, 0, -19833, 1067463]$	$y^2=x^3+x^2-19833x+1067463$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[]$
62400.ib2	62400ig1	62400.ib	62400ig	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{12} \cdot 3^{2} \cdot 5^{3} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$2.678876443$	$1$		$3$	$28672$	$0.407947$	$107850176/117$	$1.01593$	$2.86581$	$[0, 1, 0, -793, -8857]$	$y^2=x^3+x^2-793x-8857$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[(143, 1680)]$
93600.i2	93600fa1	93600.i	93600fa	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{6} \cdot 3^{8} \cdot 5^{3} \cdot 13 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$6.726747395$	$1$		$11$	$57344$	$0.610680$	$107850176/117$	$1.01593$	$2.97683$	$[0, 0, 0, -1785, -29000]$	$y^2=x^3-1785x-29000$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[(-24, 4), (56, 216)]$
93600.m2	93600cn1	93600.m	93600cn	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{6} \cdot 3^{8} \cdot 5^{9} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$		$1$	$286720$	$1.415398$	$107850176/117$	$1.01593$	$3.82044$	$[0, 0, 0, -44625, 3625000]$	$y^2=x^3-44625x+3625000$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[]$
93600.er2	93600cm1	93600.er	93600cm	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{6} \cdot 3^{8} \cdot 5^{9} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$4$	$2$	$1$	$286720$	$1.415398$	$107850176/117$	$1.01593$	$3.82044$	$[0, 0, 0, -44625, -3625000]$	$y^2=x^3-44625x-3625000$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[]$
93600.ev2	93600ey1	93600.ev	93600ey	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{6} \cdot 3^{8} \cdot 5^{3} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$		$1$	$57344$	$0.610680$	$107850176/117$	$1.01593$	$2.97683$	$[0, 0, 0, -1785, 29000]$	$y^2=x^3-1785x+29000$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[]$
187200.t2	187200f1	187200.t	187200f	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{12} \cdot 3^{8} \cdot 5^{9} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$		$1$	$1146880$	$1.761972$	$107850176/117$	$1.01593$	$3.94488$	$[0, 0, 0, -178500, 29000000]$	$y^2=x^3-178500x+29000000$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[]$
187200.bm2	187200h1	187200.bm	187200h	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{12} \cdot 3^{8} \cdot 5^{3} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$3.223050109$	$1$		$3$	$229376$	$0.957253$	$107850176/117$	$1.01593$	$3.14944$	$[0, 0, 0, -7140, -232000]$	$y^2=x^3-7140x-232000$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[(110, 560)]$
187200.pe2	187200bw1	187200.pe	187200bw	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{12} \cdot 3^{8} \cdot 5^{3} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$2.078957656$	$1$		$5$	$229376$	$0.957253$	$107850176/117$	$1.01593$	$3.14944$	$[0, 0, 0, -7140, 232000]$	$y^2=x^3-7140x+232000$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[(60, 140)]$
187200.pt2	187200cc1	187200.pt	187200cc	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{12} \cdot 3^{8} \cdot 5^{9} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$4$	$2$	$1$	$1146880$	$1.761972$	$107850176/117$	$1.01593$	$3.94488$	$[0, 0, 0, -178500, -29000000]$	$y^2=x^3-178500x-29000000$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[]$
405600.c2	405600c1	405600.c	405600c	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{6} \cdot 3^{2} \cdot 5^{9} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$		$1$	$6021120$	$2.148567$	$107850176/117$	$1.01593$	$4.06794$	$[0, -1, 0, -837958, 295246912]$	$y^2=x^3-x^2-837958x+295246912$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[]$
405600.o2	405600o1	405600.o	405600o	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{6} \cdot 3^{2} \cdot 5^{3} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1.922221680$	$1$		$3$	$1204224$	$1.343847$	$107850176/117$	$1.01593$	$3.32012$	$[0, -1, 0, -33518, -2348568]$	$y^2=x^3-x^2-33518x-2348568$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[(308, 4056)]$
405600.gq2	405600gq1	405600.gq	405600gq	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{6} \cdot 3^{2} \cdot 5^{3} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$		$1$	$1204224$	$1.343847$	$107850176/117$	$1.01593$	$3.32012$	$[0, 1, 0, -33518, 2348568]$	$y^2=x^3+x^2-33518x+2348568$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[]$
405600.hd2	405600hd1	405600.hd	405600hd	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{6} \cdot 3^{2} \cdot 5^{9} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$23.36199455$	$1$		$1$	$6021120$	$2.148567$	$107850176/117$	$1.01593$	$4.06794$	$[0, 1, 0, -837958, -295246912]$	$y^2=x^3+x^2-837958x-295246912$	2.3.0.a.1, 40.6.0.c.1, 104.6.0.?, 130.6.0.?, 520.12.0.?	$[(366916486802/5563, 221580869734518000/5563)]$

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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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