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	Semistable	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
2415.a4	2415a4	2415.a	2415a	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ - 3^{12} \cdot 5^{4} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1.914810088$	$1$		$4$	$1920$	$0.741029$	$12152722588271/53476250625$	$0.93119$	$4.11020$	$[1, 1, 1, 479, 10568]$	$y^2+xy+y=x^3+x^2+479x+10568$	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 92.12.0.?, 120.12.0.?, $\ldots$	$[(-9, 79)]$
7245.n4	7245p4	7245.n	7245p	$4$	$4$	$ 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ - 3^{18} \cdot 5^{4} \cdot 7 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1$	$1$		$0$	$15360$	$1.290335$	$12152722588271/53476250625$	$0.93119$	$4.34379$	$[1, -1, 0, 4311, -281030]$	$y^2+xy=x^3-x^2+4311x-281030$	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.5, 84.12.0.?, 276.12.0.?, $\ldots$	$[]$
12075.v4	12075s4	12075.v	12075s	$4$	$4$	$ 3 \cdot 5^{2} \cdot 7 \cdot 23 $	$ - 3^{12} \cdot 5^{10} \cdot 7 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1$	$1$		$0$	$46080$	$1.545748$	$12152722588271/53476250625$	$0.93119$	$4.43380$	$[1, 0, 1, 11974, 1297073]$	$y^2+xy+y=x^3+11974x+1297073$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 140.12.0.?, 460.12.0.?, $\ldots$	$[]$
16905.h4	16905z4	16905.h	16905z	$4$	$4$	$ 3 \cdot 5 \cdot 7^{2} \cdot 23 $	$ - 3^{12} \cdot 5^{4} \cdot 7^{7} \cdot 23 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.12.0.7	2B	$19320$	$48$	$0$	$1$	$1$		$2$	$92160$	$1.713984$	$12152722588271/53476250625$	$0.93119$	$4.48793$	$[1, 0, 0, 23470, -3554475]$	$y^2+xy=x^3+23470x-3554475$	2.3.0.a.1, 4.12.0-4.c.1.1, 644.24.0.?, 840.24.0.?, 2760.24.0.?, $\ldots$	$[]$
36225.r4	36225bp3	36225.r	36225bp	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 $	$ - 3^{18} \cdot 5^{10} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.6	2B	$19320$	$48$	$0$	$5.843273795$	$1$		$0$	$368640$	$2.095055$	$12152722588271/53476250625$	$0.93119$	$4.59771$	$[1, -1, 1, 107770, -35020978]$	$y^2+xy+y=x^3-x^2+107770x-35020978$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 420.12.0.?, 644.12.0.?, $\ldots$	$[(4189/4, 204715/4)]$
38640.cg4	38640ct3	38640.cg	38640ct	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 23 $	$ - 2^{12} \cdot 3^{12} \cdot 5^{4} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1.708923444$	$1$		$5$	$122880$	$1.434175$	$12152722588271/53476250625$	$0.93119$	$3.81877$	$[0, 1, 0, 7664, -661036]$	$y^2=x^3+x^2+7664x-661036$	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.1, 92.12.0.?, 120.12.0.?, $\ldots$	$[(140, 1782)]$
50715.bj4	50715bb3	50715.bj	50715bb	$4$	$4$	$ 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 $	$ - 3^{18} \cdot 5^{4} \cdot 7^{7} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1$	$1$		$0$	$737280$	$2.263290$	$12152722588271/53476250625$	$0.93119$	$4.64126$	$[1, -1, 0, 211230, 95970825]$	$y^2+xy=x^3-x^2+211230x+95970825$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 280.12.0.?, 644.12.0.?, $\ldots$	$[]$
55545.c4	55545f3	55545.c	55545f	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23^{2} $	$ - 3^{12} \cdot 5^{4} \cdot 7 \cdot 23^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.12.0.8	2B	$19320$	$48$	$0$	$1$	$1$		$0$	$1013760$	$2.308777$	$12152722588271/53476250625$	$0.93119$	$4.65258$	$[1, 1, 1, 253380, -126049218]$	$y^2+xy+y=x^3+x^2+253380x-126049218$	2.3.0.a.1, 4.12.0-4.c.1.2, 644.24.0.?, 840.24.0.?, 2760.24.0.?, $\ldots$	$[]$
84525.cn4	84525r3	84525.cn	84525r	$4$	$4$	$ 3 \cdot 5^{2} \cdot 7^{2} \cdot 23 $	$ - 3^{12} \cdot 5^{10} \cdot 7^{7} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$19320$	$48$	$0$	$14.55401117$	$1$		$0$	$2211840$	$2.518703$	$12152722588271/53476250625$	$0.93119$	$4.70244$	$[1, 1, 0, 586750, -444309375]$	$y^2+xy=x^3+x^2+586750x-444309375$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 168.12.0.?, 552.12.0.?, $\ldots$	$[(49396075/78, 346665523075/78)]$
115920.fb4	115920ew3	115920.fb	115920ew	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ - 2^{12} \cdot 3^{18} \cdot 5^{4} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$19320$	$48$	$0$	$4.232948633$	$1$		$3$	$983040$	$1.983482$	$12152722588271/53476250625$	$0.93119$	$4.02427$	$[0, 0, 0, 68973, 17916946]$	$y^2=x^3+68973x+17916946$	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.5, 84.12.0.?, 276.12.0.?, $\ldots$	$[(447, 11750)]$
154560.ed4	154560co3	154560.ed	154560co	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 $	$ - 2^{18} \cdot 3^{12} \cdot 5^{4} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$19320$	$48$	$0$	$10.46208363$	$1$		$1$	$983040$	$1.780750$	$12152722588271/53476250625$	$0.93119$	$3.72377$	$[0, -1, 0, 30655, -5318943]$	$y^2=x^3-x^2+30655x-5318943$	2.3.0.a.1, 4.6.0.c.1, 56.12.0-4.c.1.2, 120.12.0.?, 184.12.0.?, $\ldots$	$[(37591/15, 7110064/15)]$
154560.gi4	154560ek4	154560.gi	154560ek	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 $	$ - 2^{18} \cdot 3^{12} \cdot 5^{4} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$19320$	$48$	$0$	$0.671275113$	$1$		$11$	$983040$	$1.780750$	$12152722588271/53476250625$	$0.93119$	$3.72377$	$[0, 1, 0, 30655, 5318943]$	$y^2=x^3+x^2+30655x+5318943$	2.3.0.a.1, 4.6.0.c.1, 56.12.0-4.c.1.1, 120.12.0.?, 184.12.0.?, $\ldots$	$[(43, 2592)]$
166635.bp4	166635bs4	166635.bp	166635bs	$4$	$4$	$ 3^{2} \cdot 5 \cdot 7 \cdot 23^{2} $	$ - 3^{18} \cdot 5^{4} \cdot 7 \cdot 23^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1$	$1$		$0$	$8110080$	$2.858082$	$12152722588271/53476250625$	$0.93119$	$4.77569$	$[1, -1, 0, 2280420, 3405609301]$	$y^2+xy=x^3-x^2+2280420x+3405609301$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 280.12.0.?, 644.12.0.?, $\ldots$	$[]$
193200.f4	193200ek3	193200.f	193200ek	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 $	$ - 2^{12} \cdot 3^{12} \cdot 5^{10} \cdot 7 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1$	$4$	$2$	$1$	$2949120$	$2.238895$	$12152722588271/53476250625$	$0.93119$	$4.10719$	$[0, -1, 0, 191592, -83012688]$	$y^2=x^3-x^2+191592x-83012688$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 140.12.0.?, 460.12.0.?, $\ldots$	$[]$
253575.z4	253575z4	253575.z	253575z	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 23 $	$ - 3^{18} \cdot 5^{10} \cdot 7^{7} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$19320$	$48$	$0$	$3.823314088$	$1$		$4$	$17694720$	$3.068008$	$12152722588271/53476250625$	$0.93119$	$4.81700$	$[1, -1, 1, 5280745, 12001633872]$	$y^2+xy+y=x^3-x^2+5280745x+12001633872$	2.3.0.a.1, 4.6.0.c.1, 56.12.0-4.c.1.5, 60.12.0-4.c.1.2, 184.12.0.?, $\ldots$	$[(83, 111495)]$
270480.da4	270480da4	270480.da	270480da	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 $	$ - 2^{12} \cdot 3^{12} \cdot 5^{4} \cdot 7^{7} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.12.0.8	2B	$19320$	$48$	$0$	$6.160194232$	$1$		$3$	$5898240$	$2.407131$	$12152722588271/53476250625$	$0.93119$	$4.15811$	$[0, -1, 0, 375520, 227486400]$	$y^2=x^3-x^2+375520x+227486400$	2.3.0.a.1, 4.12.0-4.c.1.2, 644.24.0.?, 840.24.0.?, 2760.24.0.?, $\ldots$	$[(-294, 9570)]$
277725.cn4	277725cn3	277725.cn	277725cn	$4$	$4$	$ 3 \cdot 5^{2} \cdot 7 \cdot 23^{2} $	$ - 3^{12} \cdot 5^{10} \cdot 7 \cdot 23^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$19320$	$48$	$0$	$4.236238098$	$1$		$0$	$24330240$	$3.113495$	$12152722588271/53476250625$	$0.93119$	$4.82559$	$[1, 0, 1, 6334499, -15768821227]$	$y^2+xy+y=x^3+6334499x-15768821227$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 168.12.0.?, 552.12.0.?, $\ldots$	$[(179437/4, 77126369/4)]$
292215.y4	292215y3	292215.y	292215y	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 23 $	$ - 3^{12} \cdot 5^{4} \cdot 7 \cdot 11^{6} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$212520$	$48$	$0$	$10.79234963$	$1$		$0$	$2457600$	$1.939976$	$12152722588271/53476250625$	$0.93119$	$3.68714$	$[1, 1, 0, 57957, -13776462]$	$y^2+xy=x^3+x^2+57957x-13776462$	2.3.0.a.1, 4.6.0.c.1, 308.12.0.?, 644.12.0.?, 840.12.0.?, $\ldots$	$[(274933/36, 128014597/36)]$
388815.bb4	388815bb4	388815.bb	388815bb	$4$	$4$	$ 3 \cdot 5 \cdot 7^{2} \cdot 23^{2} $	$ - 3^{12} \cdot 5^{4} \cdot 7^{7} \cdot 23^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1$	$1$		$0$	$48660480$	$3.281731$	$12152722588271/53476250625$	$0.93119$	$4.85629$	$[1, 0, 0, 12415619, 43272128570]$	$y^2+xy=x^3+12415619x+43272128570$	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.1, 92.12.0.?, 120.12.0.?, $\ldots$	$[]$
408135.bl4	408135bl4	408135.bl	408135bl	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 13^{2} \cdot 23 $	$ - 3^{12} \cdot 5^{4} \cdot 7 \cdot 13^{6} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$251160$	$48$	$0$	$8.351956673$	$1$		$0$	$3686400$	$2.023502$	$12152722588271/53476250625$	$0.93119$	$3.66937$	$[1, 1, 0, 80948, 22813549]$	$y^2+xy=x^3+x^2+80948x+22813549$	2.3.0.a.1, 4.6.0.c.1, 364.12.0.?, 644.12.0.?, 840.12.0.?, $\ldots$	$[(-13751/16, 17638813/16)]$
463680.dk4	463680dk3	463680.dk	463680dk	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ - 2^{18} \cdot 3^{18} \cdot 5^{4} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$19320$	$48$	$0$	$10.19978885$	$1$		$1$	$7864320$	$2.330055$	$12152722588271/53476250625$	$0.93119$	$3.91544$	$[0, 0, 0, 275892, -143335568]$	$y^2=x^3+275892x-143335568$	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.4, 168.12.0.?, 552.12.0.?, $\ldots$	$[(72289/12, 19060975/12)]$
463680.el4	463680el4	463680.el	463680el	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ - 2^{18} \cdot 3^{18} \cdot 5^{4} \cdot 7 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1$	$4$	$2$	$1$	$7864320$	$2.330055$	$12152722588271/53476250625$	$0.93119$	$3.91544$	$[0, 0, 0, 275892, 143335568]$	$y^2=x^3+275892x+143335568$	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.4, 168.12.0.?, 552.12.0.?, $\ldots$	$[]$

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Classical	Maass
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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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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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