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 (24 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
2072.a2	2072e2	2072.a	2072e	$2$	$2$	$ 2^{3} \cdot 7 \cdot 37 $	$ - 2^{8} \cdot 7 \cdot 37^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$1$		$1$	$4896$	$1.254314$	$-2065624967846736/17960084863$	$1.06882$	$5.34611$	$[0, 0, 0, -16847, -847950]$	$y^2=x^3-16847x-847950$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[]$
4144.b2	4144d2	4144.b	4144d	$2$	$2$	$ 2^{4} \cdot 7 \cdot 37 $	$ - 2^{8} \cdot 7 \cdot 37^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$1$		$1$	$9792$	$1.254314$	$-2065624967846736/17960084863$	$1.06882$	$4.90122$	$[0, 0, 0, -16847, 847950]$	$y^2=x^3-16847x+847950$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[]$
14504.f2	14504h2	14504.f	14504h	$2$	$2$	$ 2^{3} \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 7^{7} \cdot 37^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$2.534809823$	$1$		$5$	$235008$	$2.227268$	$-2065624967846736/17960084863$	$1.06882$	$5.47890$	$[0, 0, 0, -825503, 290846850]$	$y^2=x^3-825503x+290846850$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[(525, 1470)]$
16576.o2	16576d2	16576.o	16576d	$2$	$2$	$ 2^{6} \cdot 7 \cdot 37 $	$ - 2^{14} \cdot 7 \cdot 37^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$4$	$2$	$1$	$78336$	$1.600887$	$-2065624967846736/17960084863$	$1.06882$	$4.62994$	$[0, 0, 0, -67388, -6783600]$	$y^2=x^3-67388x-6783600$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[]$
16576.p2	16576q2	16576.p	16576q	$2$	$2$	$ 2^{6} \cdot 7 \cdot 37 $	$ - 2^{14} \cdot 7 \cdot 37^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$1$		$1$	$78336$	$1.600887$	$-2065624967846736/17960084863$	$1.06882$	$4.62994$	$[0, 0, 0, -67388, 6783600]$	$y^2=x^3-67388x+6783600$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[]$
18648.bf2	18648h2	18648.bf	18648h	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 37 $	$ - 2^{8} \cdot 3^{6} \cdot 7 \cdot 37^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$4$	$2$	$1$	$156672$	$1.803619$	$-2065624967846736/17960084863$	$1.06882$	$4.82188$	$[0, 0, 0, -151623, 22894650]$	$y^2=x^3-151623x+22894650$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[]$
29008.k2	29008d2	29008.k	29008d	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 7^{7} \cdot 37^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$25$	$5$	$1$	$470016$	$2.227268$	$-2065624967846736/17960084863$	$1.06882$	$5.10930$	$[0, 0, 0, -825503, -290846850]$	$y^2=x^3-825503x-290846850$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[]$
37296.cm2	37296bd2	37296.cm	37296bd	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 37 $	$ - 2^{8} \cdot 3^{6} \cdot 7 \cdot 37^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$31.16947554$	$1$		$1$	$313344$	$1.803619$	$-2065624967846736/17960084863$	$1.06882$	$4.50438$	$[0, 0, 0, -151623, -22894650]$	$y^2=x^3-151623x-22894650$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[(72038153288961/372250, 321234008805821296791/372250)]$
51800.m2	51800b2	51800.m	51800b	$2$	$2$	$ 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 $	$ - 2^{8} \cdot 5^{6} \cdot 7 \cdot 37^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$9.916926335$	$1$		$1$	$391680$	$2.059032$	$-2065624967846736/17960084863$	$1.06882$	$4.65041$	$[0, 0, 0, -421175, -105993750]$	$y^2=x^3-421175x-105993750$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[(4427719/39, 9061838128/39)]$
76664.e2	76664c2	76664.e	76664c	$2$	$2$	$ 2^{3} \cdot 7 \cdot 37^{2} $	$ - 2^{8} \cdot 7 \cdot 37^{12} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$115.0772381$	$1$		$1$	$6697728$	$3.059772$	$-2065624967846736/17960084863$	$1.06882$	$5.55604$	$[0, 0, 0, -23063543, -42951211350]$	$y^2=x^3-23063543x-42951211350$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[(127156062763397936272870903102671675870733181362431/150260867562346015551845, 257985237337747985166856070561480160031698524821868962085382352256726221296/150260867562346015551845)]$
103600.bd2	103600e2	103600.bd	103600e	$2$	$2$	$ 2^{4} \cdot 5^{2} \cdot 7 \cdot 37 $	$ - 2^{8} \cdot 5^{6} \cdot 7 \cdot 37^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$1$		$1$	$783360$	$2.059032$	$-2065624967846736/17960084863$	$1.06882$	$4.37129$	$[0, 0, 0, -421175, 105993750]$	$y^2=x^3-421175x+105993750$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[]$
116032.s2	116032bi2	116032.s	116032bi	$2$	$2$	$ 2^{6} \cdot 7^{2} \cdot 37 $	$ - 2^{14} \cdot 7^{7} \cdot 37^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$1$		$1$	$3760128$	$2.573841$	$-2065624967846736/17960084863$	$1.06882$	$4.85856$	$[0, 0, 0, -3302012, -2326774800]$	$y^2=x^3-3302012x-2326774800$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[]$
116032.t2	116032l2	116032.t	116032l	$2$	$2$	$ 2^{6} \cdot 7^{2} \cdot 37 $	$ - 2^{14} \cdot 7^{7} \cdot 37^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$0.787535851$	$1$		$7$	$3760128$	$2.573841$	$-2065624967846736/17960084863$	$1.06882$	$4.85856$	$[0, 0, 0, -3302012, 2326774800]$	$y^2=x^3-3302012x+2326774800$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[(638, 21904)]$
130536.h2	130536bm2	130536.h	130536bm	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 3^{6} \cdot 7^{7} \cdot 37^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$16.44352889$	$1$		$1$	$7520256$	$2.776573$	$-2065624967846736/17960084863$	$1.06882$	$5.01650$	$[0, 0, 0, -7429527, -7852864950]$	$y^2=x^3-7429527x-7852864950$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[(267318009/122, 4316988148011/122)]$
149184.c2	149184dp2	149184.c	149184dp	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 37 $	$ - 2^{14} \cdot 3^{6} \cdot 7 \cdot 37^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$0.898221984$	$1$		$7$	$2506752$	$2.150192$	$-2065624967846736/17960084863$	$1.06882$	$4.32932$	$[0, 0, 0, -606492, 183157200]$	$y^2=x^3-606492x+183157200$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[(469, 1369)]$
149184.m2	149184c2	149184.m	149184c	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 37 $	$ - 2^{14} \cdot 3^{6} \cdot 7 \cdot 37^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$6.163446767$	$1$		$3$	$2506752$	$2.150192$	$-2065624967846736/17960084863$	$1.06882$	$4.32932$	$[0, 0, 0, -606492, -183157200]$	$y^2=x^3-606492x-183157200$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[(18808, 2577124)]$
153328.n2	153328q2	153328.n	153328q	$2$	$2$	$ 2^{4} \cdot 7 \cdot 37^{2} $	$ - 2^{8} \cdot 7 \cdot 37^{12} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$25$	$5$	$1$	$13395456$	$3.059772$	$-2065624967846736/17960084863$	$1.06882$	$5.23351$	$[0, 0, 0, -23063543, 42951211350]$	$y^2=x^3-23063543x+42951211350$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[]$
250712.c2	250712c2	250712.c	250712c	$2$	$2$	$ 2^{3} \cdot 7 \cdot 11^{2} \cdot 37 $	$ - 2^{8} \cdot 7 \cdot 11^{6} \cdot 37^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$5.284562306$	$1$		$1$	$6266880$	$2.453262$	$-2065624967846736/17960084863$	$1.06882$	$4.44107$	$[0, 0, 0, -2038487, 1128621450]$	$y^2=x^3-2038487x+1128621450$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[(3201/2, 25047/2)]$
261072.c2	261072c2	261072.c	261072c	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 3^{6} \cdot 7^{7} \cdot 37^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$7.439544759$	$1$		$1$	$15040512$	$2.776573$	$-2065624967846736/17960084863$	$1.06882$	$4.73772$	$[0, 0, 0, -7429527, 7852864950]$	$y^2=x^3-7429527x+7852864950$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[(7281/2, 151857/2)]$
350168.g2	350168g2	350168.g	350168g	$2$	$2$	$ 2^{3} \cdot 7 \cdot 13^{2} \cdot 37 $	$ - 2^{8} \cdot 7 \cdot 13^{6} \cdot 37^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$36.48764776$	$1$		$1$	$10575360$	$2.536789$	$-2065624967846736/17960084863$	$1.06882$	$4.40336$	$[0, 0, 0, -2847143, -1862946150]$	$y^2=x^3-2847143x-1862946150$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[(1672062662436218439/7786915, 2157967383004936400734678512/7786915)]$
362600.bl2	362600bl2	362600.bl	362600bl	$2$	$2$	$ 2^{3} \cdot 5^{2} \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 5^{6} \cdot 7^{7} \cdot 37^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$2.376340304$	$1$		$3$	$18800640$	$3.031986$	$-2065624967846736/17960084863$	$1.06882$	$4.85557$	$[0, 0, 0, -20637575, 36355856250]$	$y^2=x^3-20637575x+36355856250$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[(3075, 44400)]$
414400.ck2	414400ck2	414400.ck	414400ck	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 7 \cdot 37 $	$ - 2^{14} \cdot 5^{6} \cdot 7 \cdot 37^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$1$		$1$	$6266880$	$2.405605$	$-2065624967846736/17960084863$	$1.06882$	$4.22432$	$[0, 0, 0, -1684700, 847950000]$	$y^2=x^3-1684700x+847950000$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[]$
414400.di2	414400di2	414400.di	414400di	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 7 \cdot 37 $	$ - 2^{14} \cdot 5^{6} \cdot 7 \cdot 37^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$4$	$2$	$1$	$6266880$	$2.405605$	$-2065624967846736/17960084863$	$1.06882$	$4.22432$	$[0, 0, 0, -1684700, -847950000]$	$y^2=x^3-1684700x-847950000$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[]$
466200.es2	466200es2	466200.es	466200es	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 37 $	$ - 2^{8} \cdot 3^{6} \cdot 5^{6} \cdot 7 \cdot 37^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1036$	$12$	$0$	$2.391069349$	$1$		$3$	$12533760$	$2.608337$	$-2065624967846736/17960084863$	$1.06882$	$4.37259$	$[0, 0, 0, -3790575, 2861831250]$	$y^2=x^3-3790575x+2861831250$	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[(1450, 20350)]$

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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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