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.h4	11424q4	11424.h	11424q	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{12} \cdot 3^{4} \cdot 7^{8} \cdot 17 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.50	2B	$136$	$48$	$0$	$1$	$1$		$3$	$28672$	$1.275341$	$1919569026752/7938130977$	$1.08186$	$4.11161$	$[0, -1, 0, 4143, -255807]$	$y^2=x^3-x^2+4143x-255807$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.1, 68.24.0-68.h.1.2, 136.48.0.?	$[]$
11424.u4	11424u4	11424.u	11424u	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{12} \cdot 3^{4} \cdot 7^{8} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.60	2B	$136$	$48$	$0$	$1$	$1$		$1$	$28672$	$1.275341$	$1919569026752/7938130977$	$1.08186$	$4.11161$	$[0, 1, 0, 4143, 255807]$	$y^2=x^3+x^2+4143x+255807$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.p.1.3, 68.24.0-68.h.1.1, 136.48.0.?	$[]$
22848.f4	22848bz1	22848.f	22848bz	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{6} \cdot 3^{4} \cdot 7^{8} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.101	2B	$136$	$48$	$0$	$4.305546670$	$1$		$3$	$28672$	$0.928768$	$1919569026752/7938130977$	$1.08186$	$3.41328$	$[0, -1, 0, 1036, 31458]$	$y^2=x^3-x^2+1036x+31458$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.5, 68.12.0.h.1, 136.48.0.?	$[(43, 392)]$
22848.by4	22848cy1	22848.by	22848cy	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{6} \cdot 3^{4} \cdot 7^{8} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.103	2B	$136$	$48$	$0$	$1.728745761$	$1$		$3$	$28672$	$0.928768$	$1919569026752/7938130977$	$1.08186$	$3.41328$	$[0, 1, 0, 1036, -31458]$	$y^2=x^3+x^2+1036x-31458$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.7, 68.12.0.h.1, 136.48.0.?	$[(217, 3234)]$
34272.e4	34272j2	34272.e	34272j	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 17 $	$ - 2^{12} \cdot 3^{10} \cdot 7^{8} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$408$	$48$	$0$	$1$	$1$		$1$	$229376$	$1.824648$	$1919569026752/7938130977$	$1.08186$	$4.31028$	$[0, 0, 0, 37284, -6869504]$	$y^2=x^3+37284x-6869504$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 12.12.0-4.c.1.1, 24.24.0-8.p.1.6, $\ldots$	$[]$
34272.m4	34272q2	34272.m	34272q	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 17 $	$ - 2^{12} \cdot 3^{10} \cdot 7^{8} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$408$	$48$	$0$	$1.106807031$	$1$		$5$	$229376$	$1.824648$	$1919569026752/7938130977$	$1.08186$	$4.31028$	$[0, 0, 0, 37284, 6869504]$	$y^2=x^3+37284x+6869504$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 12.12.0-4.c.1.2, 24.24.0-8.p.1.8, $\ldots$	$[(-44, 2268)]$
68544.dw4	68544dn1	68544.dw	68544dn	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 17 $	$ - 2^{6} \cdot 3^{10} \cdot 7^{8} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$408$	$48$	$0$	$14.54959960$	$1$		$1$	$229376$	$1.478073$	$1919569026752/7938130977$	$1.08186$	$3.66849$	$[0, 0, 0, 9321, -858688]$	$y^2=x^3+9321x-858688$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 24.24.0-8.p.1.7, 68.12.0.h.1, $\ldots$	$[(5133769/130, 12034356147/130)]$
68544.eb4	68544el1	68544.eb	68544el	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 17 $	$ - 2^{6} \cdot 3^{10} \cdot 7^{8} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$408$	$48$	$0$	$1$	$1$		$1$	$229376$	$1.478073$	$1919569026752/7938130977$	$1.08186$	$3.66849$	$[0, 0, 0, 9321, 858688]$	$y^2=x^3+9321x+858688$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 24.24.0-8.p.1.5, 68.12.0.h.1, $\ldots$	$[]$
79968.k4	79968br2	79968.k	79968br	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7^{2} \cdot 17 $	$ - 2^{12} \cdot 3^{4} \cdot 7^{14} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$952$	$48$	$0$	$4.221653817$	$1$		$5$	$1376256$	$2.248295$	$1919569026752/7938130977$	$1.08186$	$4.43710$	$[0, -1, 0, 202991, -87335807]$	$y^2=x^3-x^2+202991x-87335807$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 28.12.0-4.c.1.1, 56.24.0-8.p.1.4, $\ldots$	$[(301, 972)]$
79968.br4	79968co2	79968.br	79968co	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7^{2} \cdot 17 $	$ - 2^{12} \cdot 3^{4} \cdot 7^{14} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$952$	$48$	$0$	$1$	$1$		$1$	$1376256$	$2.248295$	$1919569026752/7938130977$	$1.08186$	$4.43710$	$[0, 1, 0, 202991, 87335807]$	$y^2=x^3+x^2+202991x+87335807$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 28.12.0-4.c.1.2, 56.24.0-8.p.1.3, $\ldots$	$[]$
159936.eh4	159936ep1	159936.eh	159936ep	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{4} \cdot 7^{14} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$952$	$48$	$0$	$14.03820786$	$1$		$1$	$1376256$	$1.901724$	$1919569026752/7938130977$	$1.08186$	$3.83335$	$[0, -1, 0, 50748, 10891602]$	$y^2=x^3-x^2+50748x+10891602$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 56.24.0-8.p.1.2, 68.12.0.h.1, $\ldots$	$[(1006019/37, 1067898700/37)]$
159936.jg4	159936bw1	159936.jg	159936bw	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{4} \cdot 7^{14} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$952$	$48$	$0$	$1$	$4$	$2$	$1$	$1376256$	$1.901724$	$1919569026752/7938130977$	$1.08186$	$3.83335$	$[0, 1, 0, 50748, -10891602]$	$y^2=x^3+x^2+50748x-10891602$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 56.24.0-8.p.1.1, 68.12.0.h.1, $\ldots$	$[]$
194208.g4	194208t3	194208.g	194208t	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17^{2} $	$ - 2^{12} \cdot 3^{4} \cdot 7^{8} \cdot 17^{7} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.51	2B	$136$	$48$	$0$	$2.188252819$	$1$		$9$	$8257536$	$2.691948$	$1919569026752/7938130977$	$1.08186$	$4.55099$	$[0, -1, 0, 1197231, 1249596225]$	$y^2=x^3-x^2+1197231x+1249596225$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.8, 68.24.0-68.h.1.2, 136.48.0.?	$[(363, 41616)]$
194208.bp4	194208e3	194208.bp	194208e	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17^{2} $	$ - 2^{12} \cdot 3^{4} \cdot 7^{8} \cdot 17^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.61	2B	$136$	$48$	$0$	$2.770454501$	$1$		$3$	$8257536$	$2.691948$	$1919569026752/7938130977$	$1.08186$	$4.55099$	$[0, 1, 0, 1197231, -1249596225]$	$y^2=x^3+x^2+1197231x-1249596225$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.p.1.6, 68.24.0-68.h.1.1, 136.48.0.?	$[(4839, 343332)]$
239904.cx4	239904cx3	239904.cx	239904cx	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ - 2^{12} \cdot 3^{10} \cdot 7^{14} \cdot 17 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$2856$	$48$	$0$	$19.76189285$	$1$		$5$	$11010048$	$2.797604$	$1919569026752/7938130977$	$1.08186$	$4.57571$	$[0, 0, 0, 1826916, 2356239872]$	$y^2=x^3+1826916x+2356239872$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 68.12.0.h.1, 84.12.0.?, $\ldots$	$[(1204, 79380), (2704, 164520)]$
239904.dl4	239904dl3	239904.dl	239904dl	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ - 2^{12} \cdot 3^{10} \cdot 7^{14} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$2856$	$48$	$0$	$1$	$9$	$3$	$1$	$11010048$	$2.797604$	$1919569026752/7938130977$	$1.08186$	$4.57571$	$[0, 0, 0, 1826916, -2356239872]$	$y^2=x^3+1826916x-2356239872$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 68.12.0.h.1, 84.12.0.?, $\ldots$	$[]$
285600.dd4	285600dd3	285600.dd	285600dd	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $	$ - 2^{12} \cdot 3^{4} \cdot 5^{6} \cdot 7^{8} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$680$	$48$	$0$	$1$	$1$		$1$	$3670016$	$2.080059$	$1919569026752/7938130977$	$1.08186$	$3.82678$	$[0, -1, 0, 103567, 31768737]$	$y^2=x^3-x^2+103567x+31768737$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 20.12.0-4.c.1.1, 40.24.0-8.p.1.3, $\ldots$	$[]$
285600.dm4	285600dm3	285600.dm	285600dm	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $	$ - 2^{12} \cdot 3^{4} \cdot 5^{6} \cdot 7^{8} \cdot 17 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$680$	$48$	$0$	$14.11449404$	$1$		$5$	$3670016$	$2.080059$	$1919569026752/7938130977$	$1.08186$	$3.82678$	$[0, 1, 0, 103567, -31768737]$	$y^2=x^3+x^2+103567x-31768737$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 20.12.0-4.c.1.2, 40.24.0-8.p.1.1, $\ldots$	$[(613, 16200), (277, 4272)]$
388416.dc4	388416dc1	388416.dc	388416dc	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17^{2} $	$ - 2^{6} \cdot 3^{4} \cdot 7^{8} \cdot 17^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.107	2B	$136$	$48$	$0$	$1$	$4$	$2$	$1$	$8257536$	$2.345375$	$1919569026752/7938130977$	$1.08186$	$3.98273$	$[0, -1, 0, 299308, -156349182]$	$y^2=x^3-x^2+299308x-156349182$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.4, 68.12.0.h.1, 136.48.0.?	$[]$
388416.hu4	388416hu1	388416.hu	388416hu	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17^{2} $	$ - 2^{6} \cdot 3^{4} \cdot 7^{8} \cdot 17^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.111	2B	$136$	$48$	$0$	$1$	$1$		$1$	$8257536$	$2.345375$	$1919569026752/7938130977$	$1.08186$	$3.98273$	$[0, 1, 0, 299308, 156349182]$	$y^2=x^3+x^2+299308x+156349182$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.2, 68.12.0.h.1, 136.48.0.?	$[]$
479808.de4	479808de1	479808.de	479808de	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{10} \cdot 7^{14} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$2856$	$48$	$0$	$8.655475822$	$1$		$1$	$11010048$	$2.451031$	$1919569026752/7938130977$	$1.08186$	$4.01532$	$[0, 0, 0, 456729, -294529984]$	$y^2=x^3+456729x-294529984$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 68.12.0.h.1, 136.24.0.?, $\ldots$	$[(15481/2, 1950507/2)]$
479808.et4	479808et1	479808.et	479808et	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{10} \cdot 7^{14} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$2856$	$48$	$0$	$13.48084184$	$1$		$1$	$11010048$	$2.451031$	$1919569026752/7938130977$	$1.08186$	$4.01532$	$[0, 0, 0, 456729, 294529984]$	$y^2=x^3+456729x+294529984$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 68.12.0.h.1, 136.24.0.?, $\ldots$	$[(1388864/35, 2042636112/35)]$

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Classical	Maass
Hilbert	Bianchi

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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