LMFDB - Elliptic curves over $\Q$ of conductor 1430

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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	Manin constant

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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
1430.a1	1430a1	1430.a	1430a	$1$	$1$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{7} \cdot 5 \cdot 11 \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$440$	$2$	$0$	$0.496493395$	$1$		$4$	$224$	$-0.144768$	$2053225511/1189760$	$0.93592$	$2.95133$	$[1, 1, 0, 27, 13]$	$y^2+xy=x^3+x^2+27x+13$	440.2.0.?	$[(1, 6)]$
1430.b1	1430b1	1430.b	1430b	$1$	$1$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{19} \cdot 5^{7} \cdot 11 \cdot 13^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$440$	$2$	$0$	$1$	$1$		$0$	$51072$	$2.633495$	$-135412551115258010417641/367535633653760000000$	$1.02578$	$7.57028$	$[1, 1, 0, -1069822, -1016405644]$	$y^2+xy=x^3+x^2-1069822x-1016405644$	440.2.0.?	$[ ]$
1430.c1	1430d3	1430.c	1430d	$3$	$9$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{9} \cdot 5 \cdot 11^{9} \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	9.24.0.3	3B.1.2	$51480$	$144$	$3$	$8.801303244$	$1$		$0$	$7776$	$1.693872$	$-89783052551043953401/1020142489034240$	$0.98506$	$6.32631$	$[1, 0, 1, -93288, -11081802]$	$y^2+xy+y=x^3-93288x-11081802$	3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 117.72.0.?, 440.2.0.?, 1320.16.0.?, $\ldots$	$[(17587/6, 1620205/6)]$
1430.c2	1430d1	1430.c	1430d	$3$	$9$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ - 2 \cdot 5^{9} \cdot 11 \cdot 13^{2} $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	9.24.0.1	3B.1.1	$51480$	$144$	$3$	$0.977922582$	$1$		$6$	$864$	$0.595261$	$-12814546750201/7261718750$	$0.91162$	$4.24810$	$[1, 0, 1, -488, 5788]$	$y^2+xy+y=x^3-488x+5788$	3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 117.72.0.?, 440.2.0.?, 1320.16.0.?, $\ldots$	$[(-26, 45)]$
1430.c3	1430d2	1430.c	1430d	$3$	$9$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{3} \cdot 5^{3} \cdot 11^{3} \cdot 13^{6} $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.24.0.1	3Cs.1.1	$51480$	$144$	$3$	$2.933767748$	$1$		$6$	$2592$	$1.144567$	$6497225437879799/6424482779000$	$0.95879$	$5.01142$	$[1, 0, 1, 3887, -78212]$	$y^2+xy+y=x^3+3887x-78212$	3.24.0-3.a.1.1, 117.72.0.?, 440.2.0.?, 1320.48.1.?, 51480.144.3.?	$[(122, 1427)]$
1430.d1	1430c2	1430.d	1430c	$2$	$2$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ 2^{5} \cdot 5^{2} \cdot 11^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$		$0$	$960$	$0.460298$	$1205943158724121/1258400$	$0.93093$	$4.77963$	$[1, 1, 0, -2217, 39269]$	$y^2+xy=x^3+x^2-2217x+39269$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[ ]$
1430.d2	1430c1	1430.d	1430c	$2$	$2$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{10} \cdot 5 \cdot 11 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$		$1$	$480$	$0.113724$	$-287626699801/9518080$	$0.87035$	$3.63923$	$[1, 1, 0, -137, 581]$	$y^2+xy=x^3+x^2-137x+581$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[ ]$
1430.e1	1430k1	1430.e	1430k	$1$	$1$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{13} \cdot 5^{5} \cdot 11^{3} \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$440$	$2$	$0$	$0.009739866$	$1$		$28$	$6240$	$1.138571$	$-3158470573163361/5758438400000$	$0.98240$	$5.10804$	$[1, -1, 1, -3057, 133281]$	$y^2+xy+y=x^3-x^2-3057x+133281$	440.2.0.?	$[(591, 14004)]$
1430.f1	1430g4	1430.f	1430g	$4$	$6$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ 2 \cdot 5^{6} \cdot 11^{2} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$17160$	$96$	$1$	$1$	$1$		$0$	$4608$	$1.093002$	$1418098748958579169/8307406250$	$1.04337$	$5.75270$	$[1, 0, 0, -23406, -1380230]$	$y^2+xy=x^3-23406x-1380230$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 104.6.0.?, 220.6.0.?, $\ldots$	$[ ]$
1430.f2	1430g3	1430.f	1430g	$4$	$6$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{2} \cdot 5^{3} \cdot 11 \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$17160$	$96$	$1$	$1$	$1$		$1$	$2304$	$0.746429$	$-327495950129089/26547449500$	$1.01229$	$4.61825$	$[1, 0, 0, -1436, -22484]$	$y^2+xy=x^3-1436x-22484$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 104.6.0.?, 110.6.0.?, $\ldots$	$[ ]$
1430.f3	1430g2	1430.f	1430g	$4$	$6$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ 2^{3} \cdot 5^{2} \cdot 11^{6} \cdot 13 $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$17160$	$96$	$1$	$1$	$1$		$4$	$1536$	$0.543697$	$7962857630209/4606058600$	$1.01501$	$4.08865$	$[1, 0, 0, -416, -104]$	$y^2+xy=x^3-416x-104$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 104.6.0.?, 220.6.0.?, $\ldots$	$[ ]$
1430.f4	1430g1	1430.f	1430g	$4$	$6$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{6} \cdot 5 \cdot 11^{3} \cdot 13^{2} $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$17160$	$96$	$1$	$1$	$1$		$5$	$768$	$0.197124$	$124326214271/71980480$	$0.99017$	$3.51613$	$[1, 0, 0, 104, 0]$	$y^2+xy=x^3+104x$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 104.6.0.?, 110.6.0.?, $\ldots$	$[ ]$
1430.g1	1430e1	1430.g	1430e	$1$	$1$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{5} \cdot 5^{3} \cdot 11 \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$440$	$2$	$0$	$0.143550622$	$1$		$8$	$480$	$0.363181$	$-90694355177089/7436000$	$0.91443$	$4.42350$	$[1, 1, 1, -936, 10633]$	$y^2+xy+y=x^3+x^2-936x+10633$	440.2.0.?	$[(19, 3)]$
1430.h1	1430h4	1430.h	1430h	$4$	$4$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ 2^{5} \cdot 5 \cdot 11^{3} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.6	2B	$5720$	$48$	$0$	$1$	$4$	$2$	$0$	$26880$	$2.258202$	$355995140004443961140387841/2768480$	$1.13919$	$8.41478$	$[1, -1, 1, -14765227, 21841461531]$	$y^2+xy+y=x^3-x^2-14765227x+21841461531$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 104.24.0.?, 220.12.0.?, $\ldots$	$[ ]$
1430.h2	1430h3	1430.h	1430h	$4$	$4$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ 2^{5} \cdot 5^{4} \cdot 11^{12} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.12.0.8	2B	$5720$	$48$	$0$	$1$	$1$		$0$	$26880$	$2.258202$	$87501897507774086005761/815991377947460000$	$1.03224$	$7.27086$	$[1, -1, 1, -924907, 339830939]$	$y^2+xy+y=x^3-x^2-924907x+339830939$	2.3.0.a.1, 4.12.0-4.c.1.2, 104.24.0.?, 440.24.0.?, 5720.48.0.?	$[ ]$
1430.h3	1430h2	1430.h	1430h	$4$	$4$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ 2^{10} \cdot 5^{2} \cdot 11^{6} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.12.0.1	2Cs	$5720$	$48$	$0$	$1$	$1$		$2$	$13440$	$1.911629$	$86912881496074271306241/7664481510400$	$1.08157$	$7.26993$	$[1, -1, 1, -922827, 341445851]$	$y^2+xy+y=x^3-x^2-922827x+341445851$	2.6.0.a.1, 4.12.0-2.a.1.1, 104.24.0.?, 220.24.0.?, 5720.48.0.?	$[ ]$
1430.h4	1430h1	1430.h	1430h	$4$	$4$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{20} \cdot 5 \cdot 11^{3} \cdot 13^{4} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.12.0.7	2B	$5720$	$48$	$0$	$1$	$1$		$3$	$6720$	$1.565056$	$-21075830718885163521/199306463150080$	$1.00386$	$6.12639$	$[1, -1, 1, -57547, 5371099]$	$y^2+xy+y=x^3-x^2-57547x+5371099$	2.3.0.a.1, 4.12.0-4.c.1.1, 104.24.0.?, 110.6.0.?, 220.24.0.?, $\ldots$	$[ ]$
1430.i1	1430f2	1430.i	1430f	$2$	$2$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ 2^{11} \cdot 5^{14} \cdot 11^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$		$0$	$19712$	$1.865036$	$211322034896126991409/19662500000000000$	$0.98992$	$6.44145$	$[1, 1, 1, -124091, 15361609]$	$y^2+xy+y=x^3+x^2-124091x+15361609$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[ ]$
1430.i2	1430f1	1430.i	1430f	$2$	$2$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{22} \cdot 5^{7} \cdot 11 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$		$1$	$9856$	$1.518463$	$81402860249195471/609157120000000$	$0.98682$	$5.70060$	$[1, 1, 1, 9029, 1144393]$	$y^2+xy+y=x^3+x^2+9029x+1144393$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[ ]$
1430.j1	1430i2	1430.j	1430i	$2$	$2$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ 2 \cdot 5^{6} \cdot 11^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$		$0$	$576$	$0.178485$	$147281603041/49156250$	$0.87576$	$3.53945$	$[1, 1, 1, -110, -335]$	$y^2+xy+y=x^3+x^2-110x-335$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[ ]$
1430.j2	1430i1	1430.j	1430i	$2$	$2$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{2} \cdot 5^{3} \cdot 11 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$		$1$	$288$	$-0.168089$	$881974079/929500$	$0.83354$	$2.83502$	$[1, 1, 1, 20, -23]$	$y^2+xy+y=x^3+x^2+20x-23$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[ ]$
1430.k1	1430j1	1430.k	1430j	$1$	$1$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ - 2 \cdot 5 \cdot 11 \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$440$	$2$	$0$	$1$	$1$		$0$	$448$	$-0.024647$	$-20145851361/3141710$	$0.86623$	$3.29848$	$[1, -1, 1, -57, 199]$	$y^2+xy+y=x^3-x^2-57x+199$	440.2.0.?	$[ ]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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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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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