LMFDB - Elliptic curves over $\Q$ of conductor 4440

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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

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Nonmax$\ \ell$	$abc$ quality	Szpiro ratio

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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
4440.a1	4440a3	4440.a	4440a	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ 2^{11} \cdot 3^{2} \cdot 5 \cdot 37^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$1480$	$48$	$0$	$3.588046854$	$1$		$3$	$8704$	$0.887976$	$724629215378/84337245$	$0.91527$	$4.15954$	$[0, -1, 0, -2376, -39060]$	$y^2=x^3-x^2-2376x-39060$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 20.12.0-4.c.1.1, 40.24.0-40.v.1.4, $\ldots$	$[(-31, 62)]$
4440.a2	4440a2	4440.a	4440a	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ 2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 37^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$1480$	$48$	$0$	$1.794023427$	$1$		$9$	$4352$	$0.541403$	$20674973956/2772225$	$0.87646$	$3.65351$	$[0, -1, 0, -576, 4860]$	$y^2=x^3-x^2-576x+4860$	2.6.0.a.1, 8.12.0-2.a.1.1, 20.12.0-2.a.1.1, 40.24.0-40.a.1.3, 148.12.0.?, $\ldots$	$[(9, 18)]$
4440.a3	4440a1	4440.a	4440a	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ 2^{8} \cdot 3^{2} \cdot 5 \cdot 37 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$1480$	$48$	$0$	$0.897011713$	$1$		$7$	$2176$	$0.194829$	$74385620944/1665$	$0.87082$	$3.64089$	$[0, -1, 0, -556, 5236]$	$y^2=x^3-x^2-556x+5236$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 20.12.0-4.c.1.2, 40.24.0-40.bb.1.9, $\ldots$	$[(13, 6)]$
4440.a4	4440a4	4440.a	4440a	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ - 2^{11} \cdot 3^{8} \cdot 5^{4} \cdot 37 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$1480$	$48$	$0$	$3.588046854$	$1$		$3$	$8704$	$0.887976$	$39849102862/151723125$	$0.92635$	$4.01886$	$[0, -1, 0, 904, 24396]$	$y^2=x^3-x^2+904x+24396$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 40.24.0-40.bb.1.14, 148.12.0.?, $\ldots$	$[(305, 5346)]$
4440.b1	4440b3	4440.b	4440b	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ 2^{11} \cdot 3^{4} \cdot 5 \cdot 37 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$4440$	$48$	$0$	$1$	$4$	$2$	$1$	$2560$	$0.763125$	$26587051663538/14985$	$0.93863$	$4.58850$	$[0, -1, 0, -7896, -267444]$	$y^2=x^3-x^2-7896x-267444$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 40.12.0-4.c.1.1, 120.24.0.?, $\ldots$	$[]$
4440.b2	4440b4	4440.b	4440b	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ 2^{11} \cdot 3 \cdot 5 \cdot 37^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$4440$	$48$	$0$	$1$	$1$		$1$	$2560$	$0.763125$	$71157653138/28112415$	$0.91047$	$3.88321$	$[0, -1, 0, -1096, 8236]$	$y^2=x^3-x^2-1096x+8236$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0-4.c.1.2, 120.24.0.?, $\ldots$	$[]$
4440.b3	4440b2	4440.b	4440b	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 37^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$4440$	$48$	$0$	$1$	$1$		$3$	$1280$	$0.416552$	$13205172676/308025$	$0.86781$	$3.60013$	$[0, -1, 0, -496, -4004]$	$y^2=x^3-x^2-496x-4004$	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0-2.a.1.1, 120.24.0.?, 148.12.0.?, $\ldots$	$[]$
4440.b4	4440b1	4440.b	4440b	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ - 2^{8} \cdot 3 \cdot 5^{4} \cdot 37 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$4440$	$48$	$0$	$1$	$1$		$1$	$640$	$0.069978$	$21296/69375$	$0.91369$	$2.87519$	$[0, -1, 0, 4, -204]$	$y^2=x^3-x^2+4x-204$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0-4.c.1.4, 120.24.0.?, $\ldots$	$[]$
4440.c1	4440e2	4440.c	4440e	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ 2^{11} \cdot 3^{2} \cdot 5 \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4440$	$12$	$0$	$1$	$1$		$1$	$1152$	$0.269455$	$296071778/61605$	$0.97319$	$3.23046$	$[0, -1, 0, -176, 780]$	$y^2=x^3-x^2-176x+780$	2.3.0.a.1, 40.6.0.b.1, 444.6.0.?, 4440.12.0.?	$[]$
4440.c2	4440e1	4440.c	4440e	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ - 2^{10} \cdot 3 \cdot 5^{2} \cdot 37 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4440$	$12$	$0$	$1$	$1$		$1$	$576$	$-0.077119$	$1431644/2775$	$0.77348$	$2.61478$	$[0, -1, 0, 24, 60]$	$y^2=x^3-x^2+24x+60$	2.3.0.a.1, 40.6.0.c.1, 222.6.0.?, 4440.12.0.?	$[]$
4440.d1	4440f1	4440.d	4440f	$1$	$1$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ - 2^{11} \cdot 3^{3} \cdot 5^{6} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$888$	$2$	$0$	$1.559041307$	$1$		$2$	$4032$	$0.698646$	$-2054487458/15609375$	$0.91300$	$3.77644$	$[0, -1, 0, -336, 9036]$	$y^2=x^3-x^2-336x+9036$	888.2.0.?	$[(41, 250)]$
4440.e1	4440g4	4440.e	4440g	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ 2^{11} \cdot 3^{3} \cdot 5^{3} \cdot 37 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$4440$	$48$	$0$	$1$	$4$	$2$	$1$	$50688$	$2.092812$	$8167450100737631904002/124875$	$1.09741$	$6.91548$	$[0, -1, 0, -5328000, 4735407852]$	$y^2=x^3-x^2-5328000x+4735407852$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 40.24.0-40.bb.1.5, 444.12.0.?, $\ldots$	$[]$
4440.e2	4440g3	4440.e	4440g	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ 2^{11} \cdot 3^{12} \cdot 5^{3} \cdot 37^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$4440$	$48$	$0$	$1$	$1$		$1$	$50688$	$2.092812$	$2085187657182084002/124500749500125$	$0.99897$	$5.93041$	$[0, -1, 0, -338000, 71739852]$	$y^2=x^3-x^2-338000x+71739852$	2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.v.1.1, 888.24.0.?, 4440.48.0.?	$[]$
4440.e3	4440g2	4440.e	4440g	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ 2^{10} \cdot 3^{6} \cdot 5^{6} \cdot 37^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$4440$	$48$	$0$	$1$	$1$		$3$	$25344$	$1.746241$	$3988023972023988004/15593765625$	$0.99748$	$5.92509$	$[0, -1, 0, -333000, 74073852]$	$y^2=x^3-x^2-333000x+74073852$	2.6.0.a.1, 4.12.0-2.a.1.1, 40.24.0-40.a.1.4, 444.24.0.?, 4440.48.0.?	$[]$
4440.e4	4440g1	4440.e	4440g	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{12} \cdot 37 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$4440$	$48$	$0$	$1$	$1$		$3$	$12672$	$1.399666$	$-3721915550952016/243896484375$	$0.95827$	$4.94206$	$[0, -1, 0, -20500, 1198852]$	$y^2=x^3-x^2-20500x+1198852$	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.bb.1.2, 222.6.0.?, 444.24.0.?, $\ldots$	$[]$
4440.f1	4440h3	4440.f	4440h	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ 2^{10} \cdot 3 \cdot 5^{8} \cdot 37 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$888$	$48$	$0$	$1$	$4$	$2$	$1$	$3584$	$0.828570$	$1846842725956/43359375$	$1.09206$	$4.18841$	$[0, 1, 0, -2576, -50160]$	$y^2=x^3+x^2-2576x-50160$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.z.1.4, $\ldots$	$[]$
4440.f2	4440h2	4440.f	4440h	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ 2^{8} \cdot 3^{2} \cdot 5^{4} \cdot 37^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$444$	$48$	$0$	$1$	$1$		$3$	$1792$	$0.481997$	$19545784144/7700625$	$0.95404$	$3.48175$	$[0, 1, 0, -356, 1344]$	$y^2=x^3+x^2-356x+1344$	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.b.1.2, 148.24.0.?, 444.48.0.?	$[]$
4440.f3	4440h1	4440.f	4440h	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ 2^{4} \cdot 3^{4} \cdot 5^{2} \cdot 37 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$888$	$48$	$0$	$1$	$1$		$3$	$896$	$0.135423$	$208583809024/74925$	$0.90851$	$3.43353$	$[0, 1, 0, -311, 2010]$	$y^2=x^3+x^2-311x+2010$	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.z.1.8, 74.6.0.?, 148.24.0.?, $\ldots$	$[]$
4440.f4	4440h4	4440.f	4440h	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ - 2^{10} \cdot 3 \cdot 5^{2} \cdot 37^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$888$	$48$	$0$	$1$	$1$		$1$	$3584$	$0.828570$	$161555647964/140562075$	$0.91892$	$3.89831$	$[0, 1, 0, 1144, 10944]$	$y^2=x^3+x^2+1144x+10944$	2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 12.24.0-12.g.1.1, 296.24.0.?, $\ldots$	$[]$
4440.g1	4440c1	4440.g	4440c	$1$	$1$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ - 2^{8} \cdot 3^{3} \cdot 5 \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1110$	$2$	$0$	$0.264634920$	$1$		$6$	$480$	$-0.145340$	$1362944/4995$	$0.77557$	$2.54146$	$[0, 1, 0, 15, -45]$	$y^2=x^3+x^2+15x-45$	1110.2.0.?	$[(3, 6)]$
4440.h1	4440d1	4440.h	4440d	$1$	$1$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ - 2^{11} \cdot 3^{6} \cdot 5 \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1480$	$2$	$0$	$1$	$1$		$0$	$1728$	$0.398645$	$-4610398322/134865$	$0.86424$	$3.56324$	$[0, 1, 0, -440, -3792]$	$y^2=x^3+x^2-440x-3792$	1480.2.0.?	$[]$
4440.i1	4440i1	4440.i	4440i	$1$	$1$	$ 2^{3} \cdot 3 \cdot 5 \cdot 37 $	$ - 2^{11} \cdot 3^{13} \cdot 5^{2} \cdot 37^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$888$	$2$	$0$	$1$	$1$		$0$	$37440$	$1.788843$	$-100389630395083682/2018931072975$	$0.98501$	$5.57327$	$[0, 1, 0, -122960, -16922592]$	$y^2=x^3+x^2-122960x-16922592$	888.2.0.?	$[]$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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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